"Reputation" is given to you by other members when they read a post they think is particular interesting or makes a good, valid point to a debate or conversation. It can also be given if you think the person has been particularly helpful to another member, or really for any reason that you deem this person deserves a special "thank-you" or "kudos" for a post well made.
To earn reputation, you need to make quality, valid posts that other people give you respect for. To GIVE reputation, you click on the little thing that looks like a snowflake between the "user is online" icon and the "report this post" icon. Click that little icon between those two, and send the persona brief note as to why you think their post deserved special recognition.
To find out who has given you reputation points, go to your User CP, and there will be a list of your most recent reputation points, who gave them to you, and the note they sent along with it.