Fission occurs when a heavy nucleus splits two or more lighter nuclei with the release of energy. The best example is the fission of Uranium 235:
\[{}^{235}_{92}U \rightarrow {}^{144}_{56}Ba + {}^{89}_{36}Kr + 3 {}^1_0n + \: Energy\]
This is the means of energy production used in nuclear power stations. Nuclear fission results in the creation of large amounts of radioactive waste.
Fusion is the means of energy production used in stars. Light nuclei are fused into heavier nuclei with the release of energy.
\[{}^1_1p \rightarrow {}^4_2 He + 2 e^{{}+{}} +2 v + \: Energy\]
where
\[p, \: e^{{}+{}} \: v\]
is a proton, positron and neutrino respectively.Nuclear fusion is difficult to reproduce on the Earth. High temperatures and powerful magnetic fields are required.