User Reputation in its simplest form is a ranking of your user's benefit to your forum. Its basis comes from the opinions of all of your forum users that choose take part in it.
Users gain and lose reputation based on how their posts are scored by other forum participants. Users with the ability to affect reputation, will either give or take aways points by approving or disapproving with a post's content.
User reputation can be a divisive element of your forum so great care should be taken before a decision is made to enable it.
All of the factors that affect a user's reputation score are found in the User Reputation section of the vBulletin Options. Please view that section of the manual for more information on controlling how users are able to affect another user's reputation.