Paul, the real answer is long, but will give you a short one:

http://en.wikipedia.org/wiki/Radical_%28chemistry%29

I don't know if this is what you wanted to hear, but free radicals occur in many places in photography. One place is development reaction, and the lifetime and fate of radicals of the electron transfer agent has a lot to do with the superadditivity of developing agents. Radical reactions are also important in aerial oxidation of developers.