Rep is short for "Reputation" and you have an opportunity to earn Rep each time you post on the site, assuming it was helpful, smart, funny, or informative in some way.
And at anytime another user may chose to hit that +Rep button on any post you may make.
Basically its a good thing to have, and the more of it you have the better.
As your reputation score climbs higher, you will get new titles displayed under your name. The first such title is "Unremarkable", you will get new titles as you build a better reputation on the site. Higher titles become harder and harder to reach
And at anytime another user may chose to hit that +Rep button on any post you may make.
Basically its a good thing to have, and the more of it you have the better.
and to quote Matt from What is +Rep? Why does it say...