When a heavy nucleus (Uranium, for example) fissions, it splits into two smaller nuclei. Two or three neutrons are also emitted. The sum of the masses of these fragments is less than the original mass. This 'missing' mass has been converted into a large amount of energy according to Einstein's equation E=mc². When the fissionable material is confined, the emitted neutrons bombard and split other nuclei, provoking a chain reaction, either controlled (as in a nuclear reactor) or uncontrolled (as in an atomic bomb).
Don't confuse fission with fusion.