Here is the full list of privileges and moderating abilities that come with reputation.
Apart from that, there isn't much use. Reputation points tickle the reward center of the brain without providing any tangible benefit that is meaningful outside the context of the site. This is called gamification, which is an easy way for someone to motivate you to do what they want (in this case, use this site) without any cost to them.
Okay, that's a somewhat cynical interpretation. Here's a happier one. You know how when you help someone, you do it out of the goodness of your heart, but when they thank you sincerely, it makes you feel good and you are more likely to do it again? The site wants to thank you for posting good questions and good answers, but the site is a robot and can only communicate in the form of numbers.