Today in photo class:
RECIPROCITY means THE TENDENCY OF FILM TO REACT A CERTAIN WAY WHEN EXPOSED TO LIGHT.
RECIPROCITY FAILURE means WHEN FILM DOES NOT REACT THAT WAY WHEN EXPOSED TO LIGHT. (As in very long exposures, etc.)
RECIPROCITY COMPENSATION means WHATEVER IT IS YOU DO TO AVOID RECIPROCITY FAILURE. (In the case of long exposures, you make the exposures even longer, for example.)
No one has ever really explained it to me before. I've been in college for three years and in photo classes since my sophomore year of high school. Admittedly I could have just toddled off and asked the internet, but honestly, I will remember what Janie Stevens calmly explains to me much, much longer than what I read off of Yahoo answers at 2 am.