Nuclear fusion is a process in which a number of smaller atomic particles are fused into a large atomic particle, releasing a considerable amount of energy in the process. Fusion occurs naturally inside stars, and many races have created artificial fusion reactions to provide energy for their own use.
For a number of years, humans were unable to create a sustained fusion reaction. As a result, humans used nuclear fission quite extensively during the 20th and 21st centuries. Humans were later able to create a sustained artificial fusion reaction, leading to the replacement of the older fission reactors. Fusion reactors became an everyday part of life in the United Federation of Planets. (TOS movie: Star Trek IV: The Voyage Home)
On space vessels, nuclear fusion reactors provided power for general use, as well as for a ship's impulse drive. On Federation starships, reactors are modular devices, which are moveable and can be brought into position depending on the energy needs of a starship. (TNG reference: Star Trek: The Next Generation Technical Manual)
By the 24th century, fusion reactors had become small enough that many homes had their own fusion reactors to provide power for their occupants. The house of Kevin and Rishon Uxbridge had a small fusion reactor, which Commander William T. Riker estimated would last another five years. (TNG episode: "The Survivors")