Fusion and fission are both energetic reactions that take place on the level of the atomic nucleus. Both processes entail the transmutation of the original element into another lighter or heavier element, and both release energy at a predictable rate. The equation used to describe the conversion of matter into energy is the same in both cases: E = mc^2.
Fusion is a way that light elements can generate energy by coming together to form a new, heavier element. Fission gives some of that energy back as a heavy element splits into daughter elements. In each case, the two lighter elements, when added together, have a mass that is somewhat less than the single atom that either started or finished the process. That difference in mass between the parent and daughter elements is what is converted to energy in either reaction. The energy is released as radiation, though the type of radiation varies by element, and can be used either to generate power as part of a controlled chain reaction or to explode with considerable force. Unfortunately, though fission is relatively easy to initiate and to control, fusion reactions require a great deal of energy to start, which has delayed the development of working fusion reactors.