nuclear fission
Nuclear fission is the splitting of a single heavy nucleus into two lighter ones, releasing a burst of energy and a few spare neutrons. Everyday image: like a bloated water balloon that a small poke causes to break into two smaller ones, spraying droplets, a heavy nucleus like uranium can be split by a neutron, flinging out energy and more neutrons. The question it answers: how can splitting one atom release so much energy, and how does a whole reactor or a bomb get going?
Precisely, when a slow neutron strikes a nucleus of uranium-235 (or plutonium-239), the nucleus becomes unstable and splits into two medium-sized fragments plus, typically, two or three free neutrons. Because the fragments are more tightly bound (closer to the iron peak of the binding-energy curve) than the original, the leftover mass is released as energy according to E = m c^2. Crucially, the freed neutrons can strike other uranium nuclei and split them too: if each split reliably triggers at least one more, you get a self-sustaining chain reaction.
Why it matters: controlled fission, where control rods soak up enough neutrons to keep the chain steady, powers nuclear reactors that supply a large share of the world's low-carbon electricity. Uncontrolled, an explosively fast chain reaction is the principle of the atomic bomb. Honest caveat: fission does not make nuclear energy from nothing; it converts a little nuclear mass into energy, and it leaves behind radioactive fragments (nuclear waste) that remain dangerous for a long time and must be safely contained.
A uranium-235 nucleus absorbing a neutron may split into barium and krypton plus three neutrons, releasing about 200 million electron-volts, roughly 50 million times the energy of burning one carbon atom in coal.
Split a heavy nucleus; spare neutrons can sustain a chain reaction.
A chain reaction only sustains itself if, on average, at least one released neutron goes on to split another nucleus; reactors keep that number right at one, while it must exceed one for a bomb.