I think the best thing to explain is the sprint finish in last years TDF with Armstrong, Kloden, Basso, Ullrich, and Landis. I guess depending on who you are explaining it too. But I thought that was really interesting not only the actual action but also story and the tatics. I mean when it comes down to it cycling has everything that most other sports have.
The right place to start might be what sport do you like and why. If they like college basketball for the upsets and the Cynderilla teams then you have got Vockler. If like sports for strategy then you have got strategy all over the place, you just have to understand it. If you like great feets get on a bike and climb a mountain, or try to cruise along at 25 mph for a hour, then watch and realize what they are doing is really impressive. If you just like action and hitting well group sprints and track racing and the occasional crash. It has got it all. Of course my brother says unlike NASCAR you feel bad when someone crashes since you know it hurts
Although this is all coming from someone who likes to watch curling.