here's a more complete explanation copied from elsewhere:
What is reputation (rep)?
There is a reputation system in which users give points to other users for good or bad posts.
Giving out reputation
You can give out reputation by clicking on the button near a post.
The number of points you give out when you rep someone (called reputation power) depends on your post count, how long you have been a member, and your own number of reputation points.
You can give out either positive or negative reputation. Positive reputation will add to the recipient's reputation points total and negative reputation will deduct from the recipient's total. If you give a negative reputation, the amount of points it will reduce the recipient's reputation total by will be half the value of your reputation power (rounded down for odd numbers).
Receiving reputation
A user's points are linked to the 'gems' you see above their posts. Everyone starts off with 10 points, or one green gem. Then, for every 100 rep points (for small reputations) you get another green gem.
If you've been given rep (not before), you can check your reputation points by clicking on User CP at the top of the page. You will see the last ten reps you have received.
The second column will direct you to the post which the person giving out the rep is referring to.
The third column is for any comment made by the person giving out the rep.
If you pass your cursor over your gem/gems above one of your posts or in your profile, you'll see a message come up. This message refers to the number of rep points you have. The higher the number of rep points, the greater your rep status
