Reputation defined by Vbulletin:
The User Reputation system allows your board members to leave comments about one anothers' posts, and thereby contribute to their overall 'reputation'.
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.
OK, now that it is defined lets look a some examples:
First thing we do is look for the reputation button. This button is a little scale located at the top right hand corner of the users post

Once you click on the reputation button the follow screen will come up

Fill in the comment with a quick summary of why you approve or disapprove of the post the user made.
FAQ
How do I see my latest rep stats?
You can check your own reputation by going to the
control panel and scrolling down to the very bottom where it says "Latest Reputation Received". This will show the last reps given and your total score.
What else decides my rep level?
Register Date Factor - For every 183 number of days, you gain 1 point of reputation-altering power.
Post Count Factor - For every 25 number of posts, users gain 1 point of reputation-altering power.
Reputation Point Factor - For every 10 points of reputation, users gain 1 point of reputation-altering power.
Are there a limit of reps I can give?
Yes. A user can give 25 reps over a 24 hour period.
How many different users must you give reputation to before you can hit the same person again?
2, administrators are exempt from this limit.