Nuclear fission is the splitting of an unstable nucleus into two lighter nuclei and several elementary particles. This splitting is accompanied by a release of heat, i.e. of energy.
Spontaneous fission exists but it is very rare. The only naturally fissile element is uranium 235. Struck by a neutron, the nucleus becomes unstable and is transformed into two lighter nuclei, also unstable, called fission products. When the neutron collides with the nucleus, these fission products are ejected at high speed. The nuclei from this fission are radioactive in most cases, but they have quite a short half life.
Fission releases a huge amount of energy. 1 gram of uranium 235 releases as much energy as the combustion of several tonnes of coal. The neutrons released by fission have very high energy. If they can be slowed down enough, they can cause further fission and the reaction continues and accelerates. In nuclear reactors, the reaction is self-sustaining. But if the number of neutrons is allowed to rise, the reaction can become explosive, which is what happens in an atomic bomb (an A bomb).