Nuclear Fission is the process by how nuclear reactors and nuclear atomic bombs (basically an uncontrolled nuclear reactor that is left to explode) work.

Generally, at the quantum level, all atoms have both a strong nuclear force, pushing inward, and another force that pushes outward. The nuclear force is the force that pulls electrons towards the nucleus of an atom and allows them to continuously circle and orbit this same nucleus. This is why electrons (with a negative charge), and protons (with a positive charge), do not repel as we would imagine would normally occur with a positively and negatively charged magnet when held near eachother.

However, let's say we fire a neutron (with no electrical charge) towards the nucleus of an atom. Since the strong nuclear force only acts on, let's say, protons or electrons that are near the nucleus with electric charges, the neutron would reach the nucleus of the atom and thus be absorbed by it.

Uranium-235 is the material generally used in atomic bombs. This is because it is generally on the cusp between almost-equal strong nuclear and the force that pushes outwards. If a neutron was to be fired into the atom of enriched uranium-235, it would become a uranium-236 atom since the neutron is absorbed into the nucleus of the atom. When a critical mass of uranium-236 is present, the nucleus and atom becomes unstable, so the nucleus splits into two different nuclei of new different elements (i.e. Kr-92, and Ba-141). Fast-moving lighter elements (the fission products created), and these now released free neutrons are no longer being pushed by a strong nuclear force that is equal to the outward-pushing force, but instead the outward-pushing force is now stronger. Thus, all of this energy and these free-moving elements/neutrons burst outward in a tremendous amount of force, energy, and power: thus the atomic bomb. Because of the neutron hitting the nucleus, this also starts a chain reaction: three neutrons are relased from this reaction, which almost instantaneously transforms over to nine released neutrons, and then gradually going from nine to 27...81...243...n(3) and so on...each successive release of neutrons equal to three times the previous amount. This tremendous amount of energy release, as stated above, is what makes nuclear fission in its uncontroled state so powerful and destructive.

I'm not sure if I fully explained all of the fundamental information regarding nuclear fission, so if there any other questions regarding it, please ask.