Those points are actually just trophies for reaching various milestones, though it's not clear if this is a feature of the forum software that was previously disabled, or something added by a plugin. I actually had them on a forum of mine a long time ago, simply because I didn't see a point in disabling them, and the software apparently did it out of the box.
The theory is that they would work kind of like Steam achievements. The notion that you're only a little bit further away from a trophy might make you more likely to engage to get that next trophy, make people compete with each other for more points in a friendly little game. See who can get the higher post count, who can get more likes on their posts, etc. Sort of making a game out of it.