In theory, it just shows how respected or liked someone is. Whenever you agree or like something someone did, or appreciate soemthing, you can hit the little rep button under their post, and leave them rep.
So that's the premise of it. When you like something, you can rep that person. Also, you can neg rep someone for being stupid, spamming, or being rude.
As for how it works, if you have 1 Rep power, and you rep someone, it adds 1 rep point to them, without taking any away from you. If you have 50 rep power, and you rep someone, it adds 50 rep points to them, again, without takign any away form you. Every time you get 100 rep points, you get 1 rep power.