Points give you an incentive to participate in eNotes, particularly in discussions. They are a way of helping you keep track of how active you have been and of how the number of your contributions compare to the number of others' contributions.
Points are used for badges from enotes. Think of them as levels or ranks that you achieve. You get points for asking questions, posting discussion topics, and responding to other people's thoughts. Check their link for more information about ways to earn points and the badges you can get for them.
It's also helpful to look at someone's points/badges if they answer one of your questions. While all members of the enotes community can assit you, check and see where your responder ranks and that might help you asses their response.
Hope this helps!