Rep power stands for reputation power and is earned a number of ways.
You can be repped, see that star looking thing in the bottom left of your post?
That's how you either rep (+) or neg (-) someone.
You also earn rep power by sticking around for a while, I think it's 1 rep power for every year you've been here.
That green bar under your username represents how many times you have been positively repped.
It also works the other way, if you're an ass and people recognize bad info you're doling out, they can neg you which will turn your bar red.
Moral of the story; it's supposed to be an indicator of basically how trustworthy you are.