There are two processes by which we can obtain energy from nuclear sources, fusion and fission. Nuclear fusion relies on energy released when a heavier element is formed by the fusion of lighter elements, for example the Sun's energy is a fusion process which occurs through the fusion of one or more hydrogen isotopes and thus creates helium. We have not yet been able to engineer usion as a continuous process.
Nuclear fission is the splitting of atomic nuclei by neutron bombardment.
As more atoms are split, more neutrons are released. This causes a chain reaction, whereby the released neutrons strike other atoms, releasing more neutrons, fission products and heat energy. This energy is converted into fuel. An uncontrolled chain reaction, such as in nuclear weapons leads to an explosion, while a controlled or stable reaction like the ones in reactors generate electricity. The first controlled nuclear fission was in 1942.