Nuclear fusion is a way of producing energy by joining two light nuclei together to get one heavier nucleus. It is nuclear fusion that powers the stars!
This animation shows a simple example of such a fusion reaction where a deuterium nucleus joins one of tritium to make one nucleus of helium 5. This is unstable and so
emits a neutron to become helium 4
21H + 31H becomes 42He + 10n +Energy
The reason that energy is produced is that the combined mass of the deuterium and tritium nuclei is slightly greater than the mass of the one helium nucleus. This tiny difference becomes energy.
You don't get as much energy produced when two nuclei fuse as you do when one nucleus of uranium splits but because deuterium is so much lighter than uranium there are many more nuclei per kilogram of material and the energy released per kilogram is actually a little more for deuterium fusion than for uranium fission.
Deuterium is found in water (since a water molecule is made of two hydrogen atoms and one oxygen atom) and in fact one atom in every 5000 atoms of hydrogen in sea water is deuterium. This means that there is a vast supply of deuterium as heavy water that could be used for fusion.