Where does the energy within atoms come from? Most kinds of energy I know about involve a finite measurement and are transferred. In other words, energy in the universe is finite and is not lost or gained but only transferred through space one way or the other. 
I was contemplating how an object, a table for instance, in order to apply enough outward force to hold an object off of the ground must have a sort of energy keeping all of its atoms together. 
Atomic bonds involve energy, I assume. 
My question is how does this energy work?


*

*where does it come from? 

*is it infinite? 

*how/why is that energy different from other kinds of energy? 


After-thought:
I notice there are some things in physics, such a gravity, that we know a whole lot about how it behaves but close to nothing about why it behaves in the first place. Perhaps this is one of those things. 
 A: First of all I recommend you to see in Internet Richard Feynman's WHY". It is exactly what he discusses, our questions about why.
An electron in an atom has two major types of energy, kinetic and potential. The first one is due to the fact that the electron performs a motion, e.g. if we calculate the average of the absolute square of the linear momentum of the electron in the ground state of a Hydrogen atom we find $< \hat {P^2} > \ = \ \frac {\hbar ^2}{a_0^2}$,
where $a_0$ is the Bohr radius.
The potential energy comes from the fact that between the electron and proton there exists an electrostatic field.
Now, why does the electron have a movement inside the atom? If the electron were localized at some time to a fix position, the uncertainty principle tells us that its linear momentum could have any value and it is not clear if the electron would remain in the atom. 
Where from comes the potential energy: there are a couple of fundamental interactions with which is endowed our universe, and the e.m. interaction is one of them, see in Internet Richard Feynman's WHY. The types I recall are e.m. interaction, strong, weak, and gravitational. As Feynman explains, the existence of these interactions are fundamental axioms of our universe.
By what the energy in atoms (molecules) differs from other energies? Gravitational energy is due to just another type of interaction with which our universe is endowed. Strong interaction is what keeps together the components that constitute the hadrons (protons and neutrons) and the residual strong interaction keeps the hadrons together in the nuclei.
