Ok, you can close your mouth now. Turns out the the guy in the video (which is a clip from the French action movie Banlieue 13, released in the US as District B13) is David Belle, the founder of Parkour.
Here is how David describes Parkour:
At the physical end, Parkour is getting over all the obstacles in your path as you would in an emergency situation. You want to move in such a way, with any movement, that will help you gain the most ground on someone/something as if escaping from someone/something or chasing toward someone/something. Also, wherever you go, you must be able to get back. If you go from A to B, you need to be able to get back from B to A. You don't need to do the same "move," but just get back.
There are a few more Parkour videos on YouTube but some of them seem more like Free running or Tricking.