When you apply your front brakes too quickly on your motorcycle and the back of the bike rises off of the ground. Stoppies are more dangerous than a wheelies because if your bike's center of gravity passes over the front wheel, you're up shit creek.

That said, there are three steps to doing a stoppie:

  1. Brake: pull in your clutch and brake hard
  2. Lunge: lunge to move the center of gravity forward
  3. Pray: pray because if it doesn't work you'll either whack your crotch into the gas tank or fly over your handlebars. If you're extremely lucky your bike won't fall on top of you.

There's really very little point in doing stoppies because your average prole (i.e. non-motorcyclist) won't be impressed.