It's a game where you push in the teeth of the alligator, with a chance that it will bite you.

It's been since my childhood since I've played it, but if I remember correctly, the goal is to push in as many teeth without the alligator triggering, and of course if it triggers, to try to pull your fingers out before you get clamped :P

It can hurt a bit if you get clamped, but it's not strong enough to do any real damage to your finger.