What does Enthalpy mean? What is meant by enthalpy? My professor tells me "heat content". That literally makes no sense. Heat content, to me, means internal energy. But clearly, that is not what enthalpy is, considering: $H=U+PV$ (and either way, they would not have had two words mean the same thing). Then, I understand that $ΔH=Q_{p}$. This statement is a mathematical formulation of the statement: "At constant pressure, enthalpy change may be interpreted as heat." Other than this, I have no idea, what $H$ or $ΔH$ means.
So what does $H$ mean?
 A: A brilliant analogy by Daniel Schroeder:


*

*To summon a rabbit the magician must "build" it with all the energy it consists of. He must provide its internal energy $U$.


*But first he must push away all the air that is in the way. This requires some work, $W=pV$. In total, the energy he must spend is $U+pV$. Let's call that enthalpy $H$:
$$H=U+pV.$$

*

*But the surroundings might help him out a bit. The warm air might provide some energy, while he is working on the summoning, by adding heat $Q=TS$. The only energy he actually has to spend himself is therefore $U+pV-TS$. Let's call this the free energy needed, or Gibbs free energy $G$:

$$G=H-TS.$$
A: Standard definition: 
Enthalpy is a measurement of energy in a thermodynamic system. It is the thermodynamic quantity equivalent to the internal energy of the system plus the product of pressure and volume.
$H=U+PV$
In a nutshell, The $U$ term can be interpreted as the energy required to create the system, and the $PV$ term as the energy that would be required to "make room" for the system if the pressure of the environment remained constant.
When a system, for example, $n$ moles of a gas of volume $V$ at pressure $P$ and temperature $T$, is created or brought to its present state from absolute zero, energy must be supplied equal to its internal energy $U$ plus $PV$, where $PV$ is the work done in pushing against the ambient (atmospheric) pressure.
More on Enthalpy :
1)  The total enthalpy, H, of a system cannot be measured directly. Enthalpy itself is a thermodynamic potential, so in order to measure the enthalpy of a system, we must refer to a defined reference point; therefore what we measure is the change in enthalpy, $\Delta H$.
2) In basic physics and statistical mechanics it may be more interesting to study the internal properties of the system and therefore the internal energy is used. But In basic chemistry, experiments are often conducted at constant atmospheric pressure, and the pressure-volume work represents an energy exchange with the atmosphere that cannot be accessed or controlled, so that $\Delta H$ is the expression chosen for the heat of reaction.
3) Energy must be supplied to remove particles from the surroundings to make space for the creation of the system, assuming that the pressure $P$ remains constant; this is the $PV$ term. The supplied energy must also provide the change in internal energy, $U$, which includes activation energies, ionization energies, mixing energies, vaporization energies, chemical bond energies, and so forth. 
Together, these constitute the change in the enthalpy $U + PV$. For systems at constant pressure, with no external work done other than the $PV$ work, the change in enthalpy is the heat received by the system.
For a simple system, with a constant number of particles, the difference in enthalpy is the maximum amount of thermal energy derivable from a thermodynamic process in which the pressure is held constant.
(Source : https://en.wikipedia.org/wiki/Enthalpy )
OP's question- 
What does "make room" mean ? -
For instance, you are sitting on a chair. Then you stand up and stretch your arms. Doing this, you displace some air to make room for yourself. Similarly a gas does some work to displace other gases or any other constraint to make room for itself. To make it more understandable, imagine yourself contained in a box just big enough to contain you. Now, trying stretching your arms. You will certainly have to do a lot of work to completely stretch you arms completely. Air is just like this box except in case of air you have to do negligible work to make room for yourself.
A: Enthalpy accounts for the energy associated with mass flow in/out of an open thermodynamic system.
The specific enthalpy h (enthalpy per unit mass) is h=u+pv where u is specific internal energy, p is pressure, and v is specific volume. In the energy balance for the open system, the energy added to/removed form the system by mass flow is accounted for considering the enthalpy in/out of the system. The pv term is called flow energy from an Eulerian viewpoint-fixed in space- as is used for an open thermodynamic system. (From a Lagrangian viewpoint- following a fixed mass- pv is called flow work.)
In general the specific energy associated with mass flow is h+V2/2+gZ where V is velocity g is the acceleration of gravity, and Z is elevation. This accounts the kinetic and potential energy per unit mass for mass flowing in/out of an open thermodynamic system in in addition to the enthalpy.
For a closed thermodynamic system (no mass flow in/out) enthalpy is associated with a constant pressure process.
For a closed system Q−W=ΔU where Q is heat added to the system, W is work done by the system, and ΔU is change in internal energy, U, of the system. For the case where heat is slowly added at constant pressure, the work done by the system is pΔV and for constant pressure this is Δ(pV). Therefore, Q=ΔH. H is the enthalpy of the system equal to U+pV where , p is pressure, and V is volume. ΔH is the change in the enthalpy of the closed system.
I suggest you consult a good text on Thermodynamics, such as one by Sonntag and Van Wylen.
A: 
Consider a cylinder containing a certain mass of gas and enclosed by a weightless piston on top.
If you heat the system, the temperature of the gas will rise resulting in an increment in the pressure of the gas. This will cause the piston on the top to rise. The expanding gas will lose some of its thermal energy while doing the above work. Similarly, the volume of the gaseous system is also increasing. The above two factors would cause the gaseous pressure to ultimately equalize with the atmospheric pressure.
If $\Delta Q$ is the amount of heat added into the gas, $\Delta W$ the work done by the gas, and $\Delta U$ the increment in the internal energy of the gas (which is proportional to the increment in temperature of the gas), then
$$\Delta Q = \Delta U + \Delta W$$
$$\Delta Q = \Delta U + P\Delta V$$
$$\Delta Q = \Delta (U + PV)$$
The change in the '$U+PV$' quantity of the system indicates the amount of heat added to the system.
This '$U+PV$' quantity of the system is what we refer to as the enthalpy of the system.
The change in the enthalpy of the system denote the heat added to the system.
$$\Delta Q = \Delta H$$
We can't numerically describe terms like $Q$, $U$, and $H$ but can only describe the change in them. This is because, the zero in such quantities are arbitrary. However, this should only be of little concern as it is the changes in the above quantities that actually interest us.
A: For me, I think what your professor says, makes sense and very simple, the main point.
I don't really get your equation (and due to it, my answer might won't be able to 'satisfy' your question according to your expectation of answer). Anyways, hear me out please.
Enthalpy is actually "energy content". But you see, the thing is, "energy" (ability to do work) is a term which is too abstract, we cannot point out what is actually an energy. Instead, scientists describe it  with 'assumptions' to show the mechanism of energy. One of those assumptions is the phenomena of heat.
Heat is something that we can feel and scientists believe that heat is a 'form' of energy, so they use heat to represent energy as they can 'measure' heat by observing the change of temperature of an object.
Currently, my level of education is pre-university and due to that, I've been told to 'assume' that it is impossible to find the energy content of a 'thing' (measure the amount of heat it carries), but I personally believe it is possible under only 'strict environment' and it would be very hard to do so. It is why the general rule is a such kind of assumption.
As the general rule is 'the exact enthalpy (energy content) of a thing is unknown', we cannot find the energy content of a thing. However, if an object experiences a certain change, for instance, the revolution of an engine becomes higher from rotating slowly initially, we can compare the heat produced from both initial and final revolution speed, thus we can deduce the enthalpy change which is the energy content change (or amount of heat change). 
It is possible to find the change of enthalpy (energy content change or amount of heat  change) if other 'variables' such as specific heat capacity, the density of water (amount of $\rm H_2O$ present in a certain volume) and pressure remain constant.
I think this is enough since you are only asking what is enthalpy and what is enthalpy change. One more thing, $H$ is the symbol of heat content and $\Delta H$ is the symbol of amount of heat change.
Points to note:


*

*Enthalpy is energy content

*Energy is a vague concept

*Heat is used to represent energy

*Thus, enthalpy is heat content

*We cannot determine what is the exact amount of energy / heat content (enthalpy, $H$) in a thing

*But we can measure the energy change / heat content (enthalpy change, $\Delta H$) which is either increased or decreased
P/s: For me, the idea of enthalpy is kinda messy, especially with the way of people explaining the idea using their so-called 'sophisticated' word.
