Nuclear fusion is the process in which two or more atoms merge to become one or more heavier elements. All atomic nuclei, being composed of protons and neutrons, repel one another because of their positive charge. However, if the atoms have a high enough temperature and pressure (as is the case in the core of suns, for example), then their random motions can overcome such electrical repulsion, and they can come close enough for the strong nuclear force to take effect, fusing them into heavier atoms. This process releases tremendeous amounts of energy, and is used in fusion reactors.
The resultant nucleus is smaller in mass than the sum of the ones that made it; the difference in mass is converted into energy by the equation E=mc2. In the case of suns, 4 hydrogen nuclei combine to form a single helium nucleus; about 0.3% of the original mass is converted into energy.