Kindle
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.
Part 1, Part 2, Part 3 (via Raph)
See also:
Theory of Fun: Understanding Comics for games
Theory of Fun PDF - UPDATED
Koster's amazing "What are the lessons of MMORPGs today?"
I write books. My latest is a YA science fiction novel called Homeland (it's the sequel to Little Brother). More books: Rapture of the Nerds (a novel, with Charlie Stross); With a Little Help (short stories); and The Great Big Beautiful Tomorrow (novella and nonfic). I speak all over the place and I tweet and tumble, too.