Fission is splitting big atoms, like Uranium and fusion is sticking together small atoms, like hydrogen. You get lots of energy doing either of them.
The problem with fission is the reaction can ‘runaway’ and get a meltdown but this can’t happen with fusion. Also, the products of fission are nasty radioactive things but the main product from fusing hydrogen is helium 🙂
As Jack says Fusion is sticking atoms together, while Fission is splitting them apart. We are quite good a Fission now and many countries make most of their electricity this way (France for instance). The problem of Fission is the harmful waste that is produced – this poses very serious health problems to people, animals and plants if not dealt with properly – but this is where Laurence’s research is very exciting.
Same answer as Jack. In nuclear fission we split large elements such as uranium and plutonium (specifically U-235 and Pu-241) to get energy whereas with fusion we push together hydrogen atoms to make helium.