First, let's define the two terms.  Fission is the breaking down of a heavy atom into smaller atoms and subatomic particles.  Fusion is the binding together of two smaller atoms into a larger atom.  Both are examples of nuclear chemistry and both produce large amounts of energy.  There are two main advantages of fusion over fission.  First, fusion reactions produce absolutely enormous amounts of energy, much more than fission reactions.  The other main advantage is that fusion does not produce radioactive, toxic waste products like fission does.  So why do we use fission reactors instead of fusion reactors?  Because so far, nobody has been able to produce a fusion reactor that produces more energy than it takes in.  Fusion produces large amounts of energy, but it also requires large amounts of energy to get started.  But if a large enough reactor could be built and gotten started with a huge input of energy, the energy produced can cause a self-sustaining reaction that could produce energy for a long time.  The Sun is probably the ultimate example of a fusion reactor.