Fission: The breaking down of a Nucleus (not atom) into smaller nuclei. It is usually induced by a neutron.

For example, a Helium nucleus (called alpha particle) is divided into two 4He(+2) --> 2H(+1) + 2H(+1)

A lot of energy is released in the process.

Fusion: This happens when two nuclei combines to form a larger nuclei. Huge amount of energy is needed to start this. Because its not easy to bring two positively charged nuclei closer.When they combine, a huge amount of energy is released.

This usually happens in the stars. The enery required to start the fusion comes from the gravitational force between the particles.