A nuclear reaction is a process involving an atomic nucleus or more than one nucleus. The most common kinds are
In the case of radioactivity the reaction is spontaneous. Fission and fusion can be done on purpose, to release energy. This energy can then be used for different things, for example to make steam (as in a nuclear power plant). It can also be used as energy for a bomb.
In the example figure 6Li fuses with deuterium. This makes Beryllium which then decays into two alpha particles.
Nuclear reactions occur in the sun, in nuclear reactors, in particle accelerators, and in outer space. Other than radioactive decay, very few nuclear reactions occur on earth except in these special places. Nuclear reactors use nuclear reactions to make heat and electricity. Accelerators sometimes cause nuclear reactions to make radioactive materials. Particles from outer space cause nuclear reactions in earth's atmosphere that make air slightly radioactive.
Nuclear reactions differ from chemical reactions in that they do not need a catalyst. Radioactive decay also cannot be stopped, sped up or slowed down.