Nuclear fusion is the process of making a single heavy nucleus (part of an atom) from two lighter nuclei. This process is called a nuclear reaction. It releases a large amount of energy.
The nucleus made by fusion is heavier than either of the starting nuclei. However, it is not as heavy as the combination of the original mass of the starting nuclei (atoms). This lost mass is changed into lots of energy. This is shown in Einstein's famous E=mc2 equation.