Where does the energy from a nuclear bomb come from? I'll break this down to two related questions:
With a fission bomb, Uranium or Plutonium atoms are split by a high energy neutron, thus releasing energy (and more neutrons). Where does the energy come from? Most books I've ever come across simply state $E=mc^2$ and leave it at that. Is it that matter (say a proton or neutron) is actually converted into energy? That would obviously affect the elements produced by the fission since there would be less matter at the end. It would also indicate exactly how energy could be released per atom given the fixed weight of a subatomic particle. I remember hearing once that the energy released is actually the binding energy that previously held the nucleus together.
With a fusion bomb, two hydrogen isotopes are pushed together to form helium and release energy - same question: where does this energy come from? Is matter actually converted or are we talking about something else here?
Sorry is this is rather basic - I haven't done physics since high school.
 A: Yes, matter of mass $m$ is directly converted to energy $E=mc^2$ which literally means that the weight of the remnants of the atomic bomb is smaller than the weight of the atomic bomb at the beginning. Fission reduces the mass by 0.1 percent or so; for fusion, you may get closer to 1 percent of mass difference.
In principle, you may release 100 percent of the $E=mc^2$ energy stored in the mass $m$ - for example by annihilation of matter with antimatter; or by creating a black hole and waiting until it evaporates into pure Hawking radiation - which is pure energy.
And yes, the differences in the energies - and the corresponding masses because $E=mc^2$ is true universally (in the rest frame), there is really just one independent quantity - may be attributed to the (changing) interaction energy between the nucleons (or quarks). Alternatively, you may imagine that the extra energy was stored in extra gluons and quark-antiquark pairs inside the nuclei. Those two descriptions are actually equivalent although this fact is not self-evident.
A: I'm not sure what you're looking for here, but I'll try a different (and simpler) approach than the other answers:
In a "traditional" chemical bomb, the energy comes from the electromagnetic force: you're breaking bonds between atoms and making more stable (lower-energy) bonds.
In a fission bomb, the energy comes from the strong nuclear force: you're breaking bonds between nucleons, producing final products that are in a lower-energy state*.
In a fusion bomb, the energy is also coming from the strong nuclear force: you're making bonds between nucleons, producing final products that are in a lower-energy state.
*To go up one level of complexity (and accuracy), Janne808 is correct: in fission bombs, the electromagnetic force is a significant contributor.  In fact, in the absence of coulomb repulsion between protons, I can't think of any fission reactions that would be exothermic.
A: Energy of a fission nuclear bomb comes from the gravitational energy of the stars.
Protons and neutrons can coalesce into different kinds of bound states. We call these states atomic nuclei. The ones with the same number of protons are called isotopes, the ones with different number are nuclei of atoms of different kinds.
There are many possible different stable states (that is, stable nuclei), with different number of nucleons and different binding energies. However there are also some general tendencies for the specific binding energy per one nucleon (proton or neutron) in the nuclei. States of simple nuclei (like hidrogen or helium) have the lowest specific nucleon binding energy amongst all elements, but the higher is the atomic number, the higher the specific energy gets. However, for the very heavy nuclei the specific binding energy starts to drop again.  
Here is a graph that sums it up:
http://en.wikipedia.org/wiki/File:Binding_energy_curve_-_common_isotopes.svg 
It means that when nucleons are in the medium-atomic number nuclei, they have the highest possible binding energy. When they sit in very light elements (hidrogen) or very heavy ones (uranium), they have weaker binding. Thus, one can say that for the low "every-day" temperatures, the very heavy elements (like the very light ones) are quasistable in a sense.
Fission bomb effectively "lets" the very heavy atomic nuclei (plutonium, or uranium) to resettle to the atoms with lower number of nucleons, that is, with higher bound energies. The released binding energy difference makes the notorious effect. In terms of the graph cited above, it corresponds to nucleons moving from the right end closer to the peak.
Yet this is not the only way to let nucleons switch to the higher binding energy state than the initial one. We can "resettle" very light elements (like hydrogen) and let nucleons move to the peak from the left. That would be fusion.
Heavy nucleons emerge in the stars. Here the gravitational energy is high enough to let the nucleons "unite" into whatever nuclei they like. Stars usually are formed from the very light elements and the nucleons inside, again, tend to get to the states with lower energies, and form more "medium-number" nuclei. The energy difference powers stars and we see the light emission, high temperatures and all other fun effects.
However, sometimes the temperatures in the stars are so high, that nucleons form the very heavy nuclei from the medium-number nuclei. even though there is no immediate "energy" benefit.
These heavy elements then disseminate everywhere with the death of the star. This stored star energy can then be released in the fission bomb.
A: Coulomb repulsion between like charges is the biggest contributor to the amount of energy released.
