Reputation points are awarded by other members for being friendly, funny, helpful, generally awesome, etc.
They basically just show new members that you're a friendly, trustworthy fellow, and all others that you're well liked in the forum's community. You can award reputation points just as they can be awarded to you.
If a member behaves distastefully, dishonestly or is just... kind of a dick, you can doll out negative reputation points by way of warning other members and permanently branding them with your disapproval. Abuse regarding reputation points will lead to warnings and ban-hammering.