What Is Energy? Where did it come from? The simplistic undergrad explanation aside, I've never really understood what energy really is. I've been told that it's something when converted from one kind of something to another kind, or does some "work", as defined by us, but what is that something?
Moreover, if the total amount of energy in the universe is finite and we cannot create energy. Then, where did it come from? I've learned from thermodynamics where it goes, but where does it come from?
I know this sounds like something trivially simple, but there is so much going on in the physical universe and I just can't grasp what it is. Maybe it is because I lack the mathematical understanding that I can't grasp the subtle things the universe is doing. Still, I want to understand what it is doing.  How do I get to the point of understanding what it's doing?
(Note: What prompted me to ask this was this answer. I'm afraid that it just puzzled me further and I sat there staring at the screen for a good 10 minutes.)
 A: Wow, this is going to be a risky answer. However, I think you may be looking for an answer that is more conceptual than mathematical or philosophical, so here goes:
Energy is change. That is, energy is present if we observe relationships between objects and fields changing in some way from moment to moment.
Heat energy is just a very fine-grained version of change, expressed in the motion of many molecules whose average motion is negligible.
Potential energy is the possibility of future change. It requires the additional idea that change can be absorbed by some sort of spring-like capability, stored for a length of time, then released again in the future as explicit change.
This spring-like storage effect always seems to boil down to some form of stretching or compressing fields in ways they don't want to go. Thus winding an old style grandfather clock with a key captures explicit change (winding) in the form of interesting stresses on the bonds that hold metal atoms together. For nuclear energy the fields are different, but the concept of stretching or compressing them in interesting ways remains pretty much the same.
Finally, within the idea of potential energy lies an important hint at the relationship between energy and mass. Mass is in a quite real sense the ultimate form of potential energy. In matter, the energy of the past is so well safeguarded from release that it takes an extraordinary key -- specifically an equal quantity and type of antimatter -- to unwind it fully and release all of its energy. For matter, it is the various unbreakable rules of conservation, such as charge conservation, that keep this energy bound up and unavailable. But if some lock-canceling antimatter does happen to show up, watch out!
Photons, the constantly-moving quanta of changing electromagnetic fields, come close to being the purest form of energy possible, with some quibbles I won't bring up here. Not surprisingly then, photons are the majority of what is released when matter and antimatter cancel each other's locks.
With that, I should emphasize again that this is not intended to be a mathematical or philosophical answer. All I'm trying to convey is that energy is all about change. It can be ongoing change, as when objects move in large unidirectional ways (kinetic) or microscopic multidirectional ways (heat), or it can be potential change. The latter is change that was captured and stashed away sometime in the past by stressing fields. The most extreme form of potential energy, one in which the release of the energy is safeguarded by profound conservation laws, is what we call matter.
A: Energy is a convenient way to account for a system's ability to do useful work. There are certain modern qualifications we attach to energy, mostly that the total energy of a closed system is always conserved (barring cosmological effects), which is now explained by the use of symmetry and Noether's theorem (as explained by other's comments).
To try to get to  a more satisfying everyday notion of energy, it is best to resort to the concept of useful work and the accounting of it.  We understand that we exert effort (force over a distance) by lifting an object from the ground to the top of a table.  For practical accounting, we need to understand how much effort was expended.  It was these sorts of accounting problems that led early engineers to the concept of energy.
Energy is useful to us only if it has the ability to change its current form into another form.  One way energy can change is to start with potential energy and convert it to kinetic energy.  For example, consider the static energy stored in the bonds of carbon and hydrogen in a gallon of gas. That bonding energy can be released and converted into useful kinetic energy, such as causing the relative motion of a car. Energy can also change from kinetic energy into potential energy and do useful work. Consider a ball rolling on a table; it has kinetic energy.  If the ball collides with a spring, compresses it, and a latch catches it, the ball will lose its kinetic energy, and the spring will gain potential energy.  
If the energy is in a form that is useless to us, then we measure it in terms of entropy.  In a closed system, there is a maximum possible value of entropy associated with it.  If the entropy of a system is lower than its maximum entropy, then that system is "not at equilibrium" and still has usable energy internal to it.  This means that work can be performed within the system to increase the multiplicity of states (which is commonly interpreted as disorder), by converting that potential energy into kinetic energy internal to itself.
In everyday terms, we only think about energy it terms of the useful work that can be derived from it.  So when we talk of selling energy in an energy market, what is being traded is a commodity that can be used to do work.  There are different ways that energy can be stored, but when we buy a certain amount of energy, we expect it to allow us to accomplish certain tasks in a predictable way.
This is a somewhat simplified discussion. There is a lot more that can be added and several clarifications are needed. I don't know your level of understanding, so I have abbreviated my explanation.
A: Energy is just a numerical quantity that never changes when nature changes its courses. It being an abstract idea can be illustrated by an analogy. And who can make you enjoy this other than Mr. Feynman. In his lectures, Feynman gave an extraordinary analogy to this:

Imagine  a  child Dennis who has  blocks  which are absolutely 
  indestructible,  and  cannot be  divided into pieces.  Each  is  the
  same  as the  other.  Let  us  suppose  that  he  has  28  blocks. 
  His  mother  puts  him  with  his 28  blocks  into  a  room at  the
  beginning  of  the  day.  At  the  end  of  the  day,  being curious, 
  she  counts  the  blocks very  carefully,  and  discovers  a 
  phenomenal law— no  matter  what  he does with the blocks,  there  are
  always  28  remaining!  This continues  for a  number of  days,  until
  one day  there  are only  27  blocks,  but  a  little investigating 
  shows  that there  is  one  under  the  rug—she must  look  everywhere
  to  be sure  that the number  of  blocks  has  not changed.  One  day,
  however,  the number  appears  to change—there are only  26  blocks. 
  Careful  investigation  indicates  that the  window  was  open,  and 
  upon looking outside,  the  other  two  blocks are  found.  Another 
  day, careful  count indicates  that there  are  30  blocks!  This
  causes  considerable  consternation,  until  it  is  realized  that 
  Bruce came to  visit, bringing  his  blocks  with  him,  and  he  left
  a few at Dennis' house.  After  she has disposed  of  the  extra
  blocks,  she  closes  the  window,  does  not  let  Bruce  in,  and 
  then everything  is  going  along all right,  until  one time  she 
  counts  and  finds  only  25 blocks.  However,  there  is  a  box  in
  the  room,  a  toy box,  and  the  mother  goes to open  the toy box, 
  but  the boy  says  "No,  do  not open  my toy  box,"  and screams.
  Mother  is  not  allowed to  open the  toy  box.  Being  extremely 
  curious,  and  somewhat ingenious,  she  invents  a  scheme!  She 
  knows  that  a block  weighs  three  ounces, so  she weighs  the box 
  at  a  time when  she  sees  28  blocks, and  it  weighs  16  ounces.
  The  next  time  she wishes  to  check,  she  weighs  the  box again, 
  subtracts  sixteen ounces  and divides  by  three.  She  discovers the
  following: 
In  the  gradual  increase  in  the  complexity  of  her  world,  she 
  finds  a  whole  series  of terms  representing  ways  of  calculating
  how many  blocks are in places  where  she is  not allowed  to look. 
  As  a  result,  she  finds  a  complex  formula,  a  quantity which
  has  to  be  computed,  which always  stays the  same  in  her
  situation.

Owing to the above analogy, it is being abstracted that energy is such a manifestation of a number which has a large number of different forms but will never change except for going in and out...
A: I don't think the answer is trivially simple. I will try to give an explanation. In many problems of physics, what you are given is the initial and final states of the system. You don't know (or maybe no one does) what happens between these two states. Now there are quantities that you can measure before and after the system has undergone this change of state. The question is can you predict some of these quantities by knowing the others. Remember that we don't know the mechanism by which the system moves from these two states. But if you have something known as a conservation law, the problem becomes simple. (By saying that a quantity is conserved we mean that it doesn't change throughout some process). Suppose you have some magic function involving the quantities, which gives the same value no matter what the state of the system is, then you are done. The value of the function we call energy. And since its value doesn't change between these two states we say that its conserved.
This excerpt is from Feynman Lectures:

There is a fact, or if you wish, a law, governing all natural phenomena that
  are known to date. There is no known exception to this law—it is exact so far as
  we know. The law is called the conservation of energy. It states that there is a
  certain quantity, which we call energy, that does not change in the manifold
  changes which nature undergoes. That is a most abstract idea, because it is a
  mathematical principle; it says that there is a numerical quantity which does not
  change when something happens. It is not a description of a mechanism, or any-
  thing concrete; it is just a strange fact that we can calculate some number and when
  we finish watching nature go through her tricks and calculate the number again,
  it is the same. (Something like the bishop on a red square, and after a number of
  moves—details unknown—it is still on some red square. It is a law of this nature.)

A: Energy is any quantity - a number with the appropriate units (in the SI system, Joules) - that is conserved as the result of the fact that the laws of physics don't depend on the time when phenomena occur, i.e. as a consequence of the time-translational symmetry. This definition, linked to Emmy Noether's fundamental theorem, is the most universal among the accurate definitions of the concept of energy.
What is the "something"? One can say that it is a number with units, a dimensionful quantity. I can't tell you that energy is a potato or another material object because it is not (although, when stored in the gasoline or any "fixed" material, the amount of energy is proportional to the amount of the material). However, when I define something as a number, it is actually a much more accurate and rigorous definition than any definition that would include potatoes. Numbers are much more well-defined and rigorous than potatoes which is why all of physics is based on mathematics and not on cooking of potatoes.
Centuries ago, before people appreciated the fundamental role of maths in physics, they believed e.g. that the heat - a form of energy - was a material called the phlogiston. But, a long long time ago experiments were done to prove that such a picture was invalid. Einstein's $E=mc^2$ partly revived the idea - energy is equivalent to mass - but even the mass in this formula has to be viewed as a number rather than something that is made out of pieces that can be "touched".
Energy has many forms - terms contributing to the total energy - that are more "concrete" than the concept of energy itself. But the very strength of the concept of energy is that it is universal and not concrete: one may convert energy from one form to another. This multiplicity of forms doesn't make the concept of energy ill-defined in any sense.
Because of energy's relationship with time above, the abstract definition of energy - the Hamiltonian - is a concept that knows all about the evolution of the physical system in time (any physical system). This fact is particularly obvious in the case of quantum mechanics where the Hamiltonian enters the Schrödinger or Heisenberg equations of motion, being put equal to a time-derivative of the state (or operators).
The total energy is conserved but it is useful because despite the conservation of the total number, the energy can have many forms, depending on the context. Energy is useful and allows us to say something about the final state from the initial state even without solving the exact problem how the system looks at any moment in between.
Work is just a process in which energy is transformed from one form (e.g. energy stored in sugars and fats in muscles) to another form (furniture's potential energy when it's being brought to the 8th floor on the staircase). That's when "work" is meant as a qualitative concept. When it's a quantitative concept, it's the amount of energy that was transformed from one form to another; in practical applications, we usually mean that it was transformed from muscles or the electrical grid or a battery or another "storage" to a form of energy that is "useful" - but of course, these labels of being "useful" are not a part of physics, they are a part of the engineering or applications (our subjective appraisals).
A: To understand what energy is, it is necessary to understand the concept of work.
Work is defined as the action of a force over a path.
$$ W=\vec{F}\cdot\vec{d}$$
What does this means? It describes how "exerting" or "draining" a particular action is. For example, imagine lifting a shopping bag of mass $10\ \mathrm{kg}$ vertically by $1\ \mathrm m$. This takes work, and exactly the following amount, given by the weight of the bag times the distance.
$$W= \vec{F}\cdot\vec{d} = Fd\cos{0}=mgd=10\ \mathrm{kg}\times9.8\ \mathrm{m\ s^{-2}}\times1\ \mathrm m=98\ \mathrm J$$
Energy is classically defined as the capacity of a physical system to do work, or in other words: as you perform work, you exchange energy for some physical effect by doing work. Or in other terms again, by exerting a force over a distance you convert energy into work.
In our example, you need to use some form of energy to lift the shopping bag. The quantity you need is exactly the amount of work we calculated.
What happens to this work? It's converted to energy again – to gravitational potential energy:
$$U_\text{final} = U_\text{initial} + W$$
or
$$\Delta U = U_\text{final} - U_\text{initial} = W = mgd$$
which is the classical definition of gravitational potential energy.
So in practice – we never see or measure energy directly. When energy changes form, it is called work, which we can measure. So work, in a way, is a "transport" concept for energy. Energy, on the other hand, is like a "reservoir" of work in potential.
Why is energy a useful quantity? After all, work seems to be a more "fundamental" quantity from an experimental point of view.
The answer to this lies in the conservation law of energy. Work in itself describes a change in energy, so it's not a conserved quantity in itself unless you embed it in the more general concept of energy, which is conserved.
In fact, we can derive large swaths of classical mechanics using conservation of energy as a prime principle, together with the principle of least action.
Caveats
In more advanced theories, conservation of energy is a much more complicated matter and does not apply as simply as in the classical sense. For example in SR, energy can be converted to apparent mass and vice versa.
There are also very interesting mathematical properties of potential energy and its relation to forces and especially fields of forces. These explanations, though are way more abstract and mathematical – I assume you want an intuitive, instinctual explanation of what energy is.
If you are looking for the former please see this question.
A: Well energy is only a part of something else that is much more important, and that is called "Action". There is a bumper sticker that reads "Physics is where the Action is". One of the most important quantities in the universe is Planck's constant, and it has the units of action.  (Joule sec). The universe is designed in such as way that the no matter how things move about or change their structure, the action changes represents the efficiency of that change. Or to put it better, the probabilities of things happening or existing can be found out by accounting for this quantity called "Action". From the principle of least action we can derive conservation laws for quantities recognisable as energy, momentum, and angular momentum, it is a consequence of the symmetries involved in the action principle. (Lubos said it better).  
Now we know that of these various kinds of conserved quantities, the energy one relates to the application of force (dear old Sir Isaac Newton figured that one out) and so the nice thing about energy is that it can be stored within structures by arranging a force to be stored. And so we have food and fuel. And chemistry. And evolution.
Chemists don't often use energy directly in calculations though, they also use a kind of minimisation principle that involves both energy and another useful quantity called entropy which is a measure of the amount of freedom of choice that we allow energy to have - this measure is called the "Free energy" and this is what allows you to calculate exactly what chemical reactions will occur and to what extent. And so it goes. This free energy is not conserved, the universe is winding down like a big clockwork spring.
The big bang (if you believe in that) is simply an earlier state when the energy density was very high. It doesn't necessarily mean that the universe was a single black hole of finite size. Quantum mechanics also tells us that there is a ground state to just about everything including spacetime, so if there is a vacuum there is a ground state energy. It is generally not worth trying to create a perpetual motion machine from the vacuum though, in spite of legendary pages of Youtube videos.
One thing that energy is not, is a kind of cosmic fluid. It is just a perspective on how change can occur - Einstein relativity theory teaches us that any kind of cosmic fluid including spiritual enlightenment fluids are impossible.
Cause effect means that there is something asymmetric that has happened. Asymmetry is closely associated with the idea of information, the problem of transferring information requires that there is a net displacement in space and time. The strictures on information transfer are the same as those on energy transfer, and we find that the movement of energy suddenly becomes about the movement of bits! So knowledge, energy and time and space must be considered in the same picture. 
Firstly the connection betwen energy and time is very profound.  We do not understand time fully but we know that our sense of real time requires there to be a meaningful succession of different states, take away clocks and time literally loses its meaning in such a context. For pure energy, every day is groundhog day - there is an intrinsic period associated with energy states but no sense of succession.
How does "real" time enter the picture? We know that there is an opportunity in spacetime for "timelike" intervals between events, in this zone a succession of events can be established that can maintain a cause-effect relationship in all reference frames. But that doesn't give us the clock itself. Systems also entangle when creating a time ordering, but this is all unclear. 
The upshot is that just as there is a energy cost to doing things in the world, there is also a "cost" for systems to even exist in the world we know - aspects of that world must be unknowable. The converse is also true, if we encounter a system that is unstable and can be stabilised by releasing specific energy, then the specificity of that energy means that the time at which the event will occur is unknowable. We simply cannot consider a concept such as energy in isolation - without understanding the nature of concepts such as knowledge and time. Its a package deal.
Finally open systems through which energy flows are better able to maintain clocks and establish a time order, so life is a phenomenon associated with unstable energy flows.
The simplest explanation that I know as to why time runs in one direction, is that events in the reverse direction are "unobservable". I know that sounds like a tautology but if you show why they are unobservable then you have a better explanation. Likewise the positive observable energy could have in its negative counterpart a reason why it is unobservable, but now I really am not qualified to comment, I have already badly exceeded my limits.
A: Any concept in physics- energy, mass, entropy- is explicitly defined by the set of mathematical relationships for the concept. Any linguistic definition of a concept is an attempt to provide a physical understanding of the concept.   For example, for force, one linguistic definition is "A description of an interaction that causes a change in an object's motion".  For me, that definition is not useful unless I understand the mathematical definition defined as F = ma and how it is used in applications.
For a broad concept like energy, the linguistic definition must necessarily be rather vague, and to understand such a definition you need to understand the mathematical relationships for energy and their use in applications.
For a basic understanding of energy, I like the simple definition of energy stated in an old engineering thermodynamics textbook.  "Energy is the capacity, either latent or apparent, to exert a force through a distance." Obert and Young, Elements of Thermodynamics and Heat Transfer. For a defined system in basic thermodynamics, we consider the internal energy, the energy in/out of the system due to work and/or heat, and the energy in/out of the system due to mass transfer. [The internal energy is sometimes called the "heat", but this is technically incorrect from a thermodynamics viewpoint.  Heat is energy that crosses a system boundary- without mass transfer- solely due to a temperature difference. Work is energy that crosses a system boundary- without mass transfer- due to  any intensive property difference other than temperature.]
Over time, the concept of energy has been extended to include rest mass energy, field energy, and so on to preserve the concept of the conservation of energy.  So again the linguistic concept has to be very broad/vague to accommodate such considerations.
Hope this helps.
A: What is energy?
Energy is the capacity of a system to do work. 
Where does it come from?
It generally comes from another source of energy, as in energy gets converted from one form to another.
Where does it ultimately come from?
That my friend is a question for MetaPhysics.stackexchange.com, which sadly doesn't exist as of now. You might want to hop over to Area51 with a proposal.
