Due to my physics background, somebody asked me to post a blog to explain how E=MC^2 relates to a chain reaction explosion. I'll try to do this quickly as it's late and I'm tired.
The formula means that energy (measured in joules) equals mass (in kilograms) times the speed of light (in meters per second) squared. This is an explanation of conservation of mass and energy. Einstein had the right idea that mass and energy, at their roots, were the same damn thing. This formula means that a tiny amount of matter can be converted into a massive amount of energy (and vice versa).
Any element more massive than lead is radioactive. When an atomic nucleus has too many protons, the electromagnetic force of the positively charged protons pushing each other apart starts to overcome the "glue" that holds them together into a nucleus. This makes the atoms unstable and prone to breaking. Uranium 235 and Plutonium 239 are particularly prone to this. Normally this happens when a chunk of nucleus is blown off from the rest of it. This is called an alpha particle and is made of two protons and two neutrons (like a helium nucleus). You can, however, get these kinds of atoms to make a more even split. This is called nuclear fission.
If I put enough of either of these two elements together (a critical mass), the natural tendancy for the nuclei to spit out particles can cause a chain reaction. Particles from one nucleus get blasted out and bump into another nucleus, causing it to blow apart, hitting the next couple, and so on. The particles that cause the chain reaction are neutrons. They have no electrical charge so are not repelled by electrons around the nucleus or the protons within it.
When the atom breaks into to pieces (usually a 2/3 chunk and a 1/3 chunk) their combined masses don't quite equal the mass of the original atom. This "mass defect" results in a release of energy via the E=MC^2 formula. You don't really lose that much mass. But the energy release is insane.
The bombs we dropped on Japan operated in this fashion. What's really freaky is the bombs we use today are a thousand times more powerful. This fission nuclear explosion is just the fuse to set off the real explosion. We use the pressure and heat from the initial nuclear explosion to cause hydrogen atoms to fuse into helium atoms (a hydrogen bomb). The mass of the two hydrogen atoms is greater than the mass of the created helium atom. Use your E=MC^2 formula again and you get a shit pot of energy released.