In a nuclear reactor there are big rods made from the element Plutonium and these rods provide fuel for the reactor. Plutonium has the ability to undergo nuclear fission, which means that individual plutonium atoms can be broken up into smaller parts. When this chemical reaction happens, a large amount of energy is released in the form of heat. The heat can then be used to produce power. However, because the reactor gets so hot, it is important to continually cool the fuel rods so that they don't melt and cause an explosion. This is what a nuclear meltdown refers to. The fuel rods must be kept cool in order to have a slow, controlled fission reaction. When the rods melt, a lot of energy is produced all at one time, resulting in an explosion (this is what happens in a nuclear bomb). Therefore, to avert a nuclear meltdown, the fission process must be stopped and the fuel rods must be cooled down.

Check out this video I found on CNN that explains what happened at the nuclear reactors in Japan after the earthquake and tsunami: