Understanding Games is a series of short animation/games that set out to explain how and why video games work — what they're composed of, how they're played, and how they're designed. It sets out to be an interactive version of the wonderful A Theory of Fun, though the title pays homage to the equally brilliant Understanding Comics.
Three of the four videos are online now, in both English and German. I really enjoyed them, though I agree with Greg Costikyan that some of the subjects are glossed over a little too lightly. Still, if you're trying to explain games to someone — a student, a loved one, your parents — this is a great way to start.