I have no idea how many points I have, though it is fun to be notified when you receive badges. They are there as a bit of an incentive to contribute often, and are, as others have said, part of the fun. At the end of the day, they are a measurement of how much help one has provided to students, and so they are certainly worthwhile.
I agree that the point system is a great motivator. It's fun to accumulate points. I remember being very happy when I reached the 50,000 point mark. My "rank" changed when I reached that mark, and I was happy about that, too. I recently answered my thousandth questions, and that, too, was a moment of satisfaction.
There are many reason why there are points. In my opinion, one of the reasons why there are point is so that the editors can have some healthy competition. This creates for editors to do a better job. Also points are given for best answers. So, if an user asks a question and he or she like a particular answer and marks it as best, then that editor gets more points. In the end, points produce better work.
The points earned is a way for enotes to keep track of how often the users and the editors contribute questions or information to the website. Various amounts of points are earned, depending upon what kind of response is given. The points don't change a user's status on the site, but there are point "thresholds" for editors to achieve different levels of achievement. Points are an interesting way for a student to see how frequently an editor contributes to a particular kind of topic, but it is not a measure of the quality of the answer. Some editors contribute often and earn a lot of points. Other editors only answer periodically, but they contribute wonderful responses too.