Why does it take so much energy to keep the protons and neutrons in an atom together I heard on the net that the reason there is so much more energy released during the breakage of an atom, i.e. the sun, than from breaking a chemical bond is because the particles are pushing away so much harder. I don't understand why a positive element pushes so hard on a neutral element. Why is there so much energy there?(Why is the repulsion in such a small space so massive) Please answer in non-sciency terms
 A: The energy released in fission is due to the electrostatic repulsion of protons.
In a nucleus like uranium, the positively-charged protons electrostatically repel each other. (With something like 20 Newtons of force! This is an enormous force on something so microscopic.) Normally the strong nuclear force manages to overcome this electrostatic repulsion, when protons and neutrons are very close together in a nucleus.
Once fission occurs by quantum tunneling through the energy barrier, the separated daughter nuclei no longer feel the nuclear force between each other, because it decreases exponentially with distance. But they still experience intense electrostatic repulsion, because the protons in one daughter nucleus repel the protons in the other daughter nucleus, and this force decreases only as the inverse-square of the distance. This electrostatic repulsion causes the daughter nuclei to move apart at high speed.
A: 
I heard on the net that the reason there is so much more energy released during the breakage of an atom, i.e. the sun, than from breaking a chemical bond is because the particles are pushing away so much harder. I don't understand why a positive element pushes so hard on a neutral element. Why is there so much energy there?

The first thing to undestand is that force and energy are two different things. "Pushing" refers to a force.
In general, the energy released in nuclear decay is equal to the difference in energy between the thing you start with and the thing(s) you end up with. These energies have three contributions: (1) kinetic energy, (2) potential energy due to the strong nuclear force, and (3) potential energy due to the electrical repulsion of the protons. In light nuclei, #3 is a small effect, so the main contributions are from #1 and #2.
1 is a big number due to the Heisenberg uncertainty principle. When you confine particles to a small space, they move violently.
2 is a big number because the strong nuclear force is strong (hence the name).
The release of energy depends on the difference between the energies of the initial and final stuff, so it's a delicate balance, and the result typically depends on details of nuclear structure. Only in certain examples, such as fission, is it possible to give a simple classical explanation of why the change in energy has one sign or the other. For fission, energy tends to be released because the electrical force is repulsive.
A: I think there's two questions in your question...

I don't understand why a positive element pushes so hard on a neutral
  element

So I'll answer that question with another question... what neutral particles?
You're going to want to say "neutrons" right? Ahhh, but what's a neutron made of? Quarks. And all of them have charges.
So it's not about protons pushing (or pulling) on neutrons, it's more like a little orgy of quarks all pushing and pulling on each other. It's actually more complex for a lot of reasons, but you get the idea.

Why is the repulsion in such a small space so massive

So basically, the force is that massive because that's how strong electricity is. It's freaking strong.
Now wait, you say, if it's so strong, why aren't I being pulled all over by the electricity in the wiring, for instance? Well, this is going to sound crazy, but it's because its so strong. Its so strong, that any loose charges that group up make such a strong force that they just grab onto other charges around them. So the forces you see aren't really the raw forces involved, its the leftover force from the microscopic differences in placement of the charges. It's so strong, you can even feel it when its completely neutral.
Here's one to ponder. The universe is electrically neutral. Think about that for a second... that means that if there was even one little electron all by itself on the left side of the universe, and a single proton on the right side, there was enough of a force that they've already met after having to travel half way across the cosmos to get there.
Want more proof? Take a piece of plastic, rub it with something fuzzy, and use the static to pick up a piece of paper. That rubbing took off a couple of electrons, and the paper is electrically neutral. Yet those few unbalanced charges creates such a strong force, that it tries to pull the atoms in the paper apart, so that their electrons end up a tiny bit closer and their protons a tiny bit further and even on that tiny tiny difference in distance results in a force that is so great that it lifts the paper against the gravity of the entire planet.
