Another question about energy(Improved) I read this thread about energy
 What Is Energy? Where did it come from?
EDIT: after some sleep I tried to read the answers again and found better questions to ask. so here you go


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*As most guys have replied in the other thread that energy should be considered mathematical rather than conceptual. 


"Energy is any quantity which can be conserved, or rather A number which remains fixed no matter what happens to a physical sys' or
Energy although being a mathematical quantity is helpful to us as it gives us useful info about the system at a particular time without knowing the mechanicsm.
As I have a kinda weak Brain this is all I could deduce from that thread.
So am I right?


*What does it mean or rather What should I visualize when someone says that energy was transferred from object' x' to object 'y'(With respect to the my above definition)


I would have asked in that thread if I could but its closed I believe
AND I hope this time I have asked the right physics question.
Edit : Mods u can close the thread.
Thanx for all your help :)
 A: The best way to approach this is to come at it from a historical & physical point of view. This is after all how the physics was discovered. Forget the maths, thats there so you can put actual numbers to the whole conception and actually do some serious calculations. It's really not necessary at this level.


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*There are different kinds of energy and they are quantifiable. For example heat, light, kinetic, gravitational etc.

*They can be sorted into two general categories 
a. one of position - this is usually referred to as potential energy. So where you stand on a hill dictates how much gravitational potential energy; where you put several electrons in space tells you how much electrical potential energy the system has etc.
b. One of motion - this is generally referred to as kinetic energy. So how quickly a stone thrown through the air moves tells you how much kinetic energy it has.

*Energy can be changed from one form into another, but the total energy of the system doesn't change. This means for example potential energy can change into kinetic energy and vice-versa, but the total amount never changes.
Work is a technical term meaning how potential energy is changed as you move things around (in 2a above).
This addresses your question by what we mean by Physics today. But to answer your question properly - that is what is it and where does it come from - is not a question of Physics as its understood today. Each time physics tries to get at the what and the where of it and resolves it to some extent - that it moves a step further back. Physics relates things, and only inquires into  what as much as it can be resolved into a question of relationships. This question is fundamentally one of metaphysics (part of philosophy), and is exceptionally intractable. 
A: Energy as a physical quantity
Energy is a physical quantity. It can be understood visually. For instance, heat can be felt and therefore this would be a good example in my eyes - in fact it can be directly measured in different cases. 
Of course there are many other forms of describing energy. This is a very short and not complete in many senses because energy is the most important quantity appearing in every field of physics. There are many other quantities that are less visually like magnetization. 
The notion of kinetic and potential energy
The explanation of MoziburUllah for the two categories was already really good. I just have to add that usually one can separate the energy terms depending on motion/momentum or on position. Therefore it is then clear which contributing term is the kinetic energy and which one is the potential energy. 
Work as a form of energy transfer
Consider a physical system in a larger environment - black box. Work is usually called the energy (transferred out of the system) in which you are interested in general, e.g. potential energy or kinetic energy of an external device/system. Further discussion about terminology is at A terminological question about work and energy.
Often the heat flow is looked as wasted energy (transferred out of the system), dissipated heat that reduces the efficiency of a process where the system is involved in. In this sense the system can be understood as a volume inside a working machine.
Remember: We are at that time not interested where the energy originally comes from (e.g. fuel) but only where it goes to.
A: Let me try to outline a possible explanation of how certain numerical parameters originating in calculations of quantum-mechanical probabilities turn into what we call the mass, the energy, and the momentum of a particle.
An important calculational tool is the (single-particle) propagator, which is used to calculate the probability with which a particle detected at spacetime point A will be detected at spacetime point B. It can be obtained by summing over all possible paths leading from A to B. Each path contributes a phase factor.
Imagine a particle that travels along one of these paths. Further imagine that the particle "ticks" whenever the phase associated with the path segment already traveled increases by 2π. Except for the units, the rate at which the particle ticks is the particle's mass. In other words, m = N/T, where N is the number of ticks produced during a proper time interval T. Multiply this by Planck's constant h to convert it into energy units. When expressed in energy units, we call it the particle's rest-energy. Divide this by the square of the speed of light c to convert it into mass units. When expressed in mass units, we call it the particle's (rest)mass.
While there is no mass other than rest mass, there is a difference between the particle's rest-energy (a.k.a. mass) and its energy. The former essentially equals ticks per units of proper time, while the latter essentially equals ticks per units of coordinate time, provided that inertial coordinates are used.
Now consider an infinitesimal path segment at (t,x,y,z) with components (dt,dx,dy,dz). It is convenient to measure the corresponding phase difference dα in units of action. The corresponding infinitesimal action then is : dS = ħ dα.
If the particle is moving freely, then dS will have no explicit dependence on (t,x,y,z). The particle will behave the same no matter where and when. If dS does not (explicitly) depend on t, dS defines a constant, and this is what we call the particle's energy. If dS does not explicitly depend on x,y,z, then dS defines another constant, the particle's momentum.
Thus by the particle's energy we mean the particular quantity which is constant because dS does not (explicitly) depend on t, and by the particle's momentum we mean the particular quantity which is constant because dS does not (explicitly) depend on x,y,z. Note that these definitions imply that the energy and the momentum of a free particle are necessarily constant.
If there are freely moving particles (that is, if we ignore spacetime curvature), and if we are interested in the classical limit, in which quantum mechanics degenerates into classical mechanics, then the only possible way we have to mathematically describe effects on the motion of a particle is to add to the action differential dS of a freely moving particle a term that is linear in the coordinate differentials:
$$-V(t,x,y,z) dt + A(t,x,y,z) dx + B(t,x,y,z) dy+ C(t,x,y,z) dz.$$
In the classical limit, in which the particle follows the path that minimizes the action, V becomes the particle's potential energy, while A,B,C become the components of the particle's potential momentum. The path that minimizes the action satisfies the Lorentz force law. This contains the components of the classical electromagnetic field, which are defined in terms of the fields V,A,B,C. If we use the Newtonian gravitation potential V (with A,B,C = 0), we similarly obtain Newton's law of gravity.
A: Your summation:

"Energy is any quantity which can be conserved, or rather A number which remains fixed no matter what happens to a physical sys' or Energy although being a mathematical quantity is helpful to us as it gives us useful info about the system at a particular time without knowing the mechanism.

Energy is not any quantity, it is a specific quantity which was identified experimentally through the centuries. The word itself comes from ancient greek, and it means "with work", ergo means work. Work at that time meant the effort spent by a person or an animal to produce something: a donkey to draw water for watering, a man to carry a weight some distance, digging the ground, etc. 
It eventually dawned on people that they could have a unit of work,( hence one gets still "horse power"), and that work could be stored and recovered : do work to put water in a cistern then take it back flushing the toilet , etc. The concepts of potential energy and kinetic energy as discussed in the other answers were identified when the empirical observations were formulated mathematically. And they also realized that energy was conserved in its various forms. It can also be stored, in chemical form ( fuels), in batteries, in dams, in nuclei.

What does it mean or rather What should I visualize when someone says that energy was transferred from object' x' to object 'y'(With respect to the my above definition)

1)a pot of water on the stove. electric energy is transferred to boiling water.
2) a boy hitting a ball with a stick: kinetic energy from his arm transfers to kinetic energy of the ball
3) A ball rolling down an incline from rest: potential energy due to gravity transformed to kinetic energy of the ball
4) a racing boat with oars: chemical energy from the bodies turns into kinetic energy of the arms and is tranferred to kinetic energy of the boat.
