To some extent, the purpose of the points varies depending upon the person looking at the points. As a general rule, the points indicate how much a person uses the website or contributes to the website. Points can be given out for a variety of things like answering homework questions, taking quizzes, and giving feedback on student essays. eNotes is always looking for ways to stay current and best help students, so not all of the things that once offered points still exist on the website. The points don't necessarily mean one Educator is better or worse than another. Two equivalently talented and knowledgeable Educators might have a vastly different number of points because one Educator might be newer to eNotes or might only answer a few questions per week. Currently, the points are tied to a "level" and title. For example, at 150,000 points, an educator would be a "Level 3 Educator Emeritus."
The points on eNotes aren't directly useful for anything. They are simply an indication of how a person uses the website. If you have friends also using eNotes, points can be used to compare how often you use it in comparison to the others.
You earn points every time you ask a question on eNotes. You earn points every time you post a reply to a discussion on eNotes. You earn notes if you can post an answer to a question asked by someone else on eNotes.
As you use the website more often, you may start looking at the number of points accumulated by various editors. The more points an editor has for a specific subject area, the more often that editor has answered questions in that area - which might mean s/he is more knowledgeable in the area.