A 'proc' is short for 'process'; this means that, under the right circumstances, your item will do something special - but a proc is subject to the laws of the Random Number Generator.
Some items proc often, some less often. AFAIK, proc rate on weapons is solely based on a certain % chance of the proc going off per swing. I've seen many, many theories about procs being per minute or DEX-based or based on time of day (RL or Norrath) - none of them seem convincing to me.