Two kinds of uranium are found in nature: non-fissile uranium-238 and, to a much lesser extent, fissile uranium-235. The numbers 235 and 238 represent the number of nuclear particles that make up the atomic nucleus of this kind of uranium. Uranium-238 is stable and is not fissile. However, Uranium-235 is unstable. If a free-moving nuclear particle (a neutron) touches this atom, the uranium-235 disintegrates. This releases energy. We call this nuclear fission. A disintegrated uranium-235 nucleus releases two or three neutrons. When they touch other uranium-235 nuclei, they disintegrate too. This causes a chain reaction, and the nuclear fuel starts producing heat from these constant nuclear fissions.
In natural uranium, the fissile uranium-235 part is so small (less than 1%) that it is not enough to generate a nuclear fission reaction. Uranium only becomes a good 'nuclear fuel' for a nuclear plant if it is a mix of around 96% uranium-238 and 4% uranium-235.
During a nuclear fission, the generated heat can be used as a source of energy. This might be to generate electricity, for example, but you can also produce hydrogen or make drinking water from sea water.
After a few years, the nuclear fuel in a reactor is used up. The debris from disintegrated uranium-235 is radioactive and accumulates in the nuclear fuel until it obstructs the chain reaction. We call this debris radioactive waste. This consists of unstable substances that are lighter than uranium, like Strontium-93 or Xenon-140. These newly formed substances are not stable and sooner or later decay to another stable substance. During this process, radiation is emitted. Once all the unstable substances have decayed to create a stable end-product, no radiation remains. Every radioactive substance decays at a different rate. For some substances this takes a few seconds, while others take thousands of years. In the Netherlands, all the radioactive waste is safely stored in the COVRA.
Nuclear fusion is a reaction in which different atoms are combined to form one heavier atomic nucleus. For nuclear fusion, the lightest atoms from nature are used, like hydrogen. In this process, some of the mass is converted into energy, around 0.67% in the case of hydrogen.
Nuclear fusion is not a chain reaction; no particles are released that could cause a new fusion. The process can only be maintained at an extremely high temperature and pressure, much higher than that at the heart of the sun. Unlike nuclear fission, nuclear fusion does not necessarily generate radioactive waste. For that reason, scientists are trying to develop nuclear fusion on Earth as a clean and safe source of energy.