The meanings mentioned by Emile are the most common, I think.
Two other meanings:
1. "De dictator werd afgezet." That translates to something like "The dictator was ousted from power."
2. "Ik heb het programma afgezet, want ik vond het verschrikkelijk." "I switched off the program, because I found it terrible." I'm not sure how to translate it better. With this wording, it's left unclear wether the person has switched off the tv or radio, or he/she simply has chosen another channel.