By default the stars are based on how many posts you have made, but the set provided are very chaotic and almost random in meaning. At present, the top tier is purple stars, the next silver and the lowest either red or black (the scheme seems to interfere with it, too).
Seems the groups take precedence over the post count. Looks like the forum system is designed to have a greater ratio of non-privilaged users. we have a number of special groups that most users are in, making a lot of it meaningless.
"Senile member" was one of of the post rankings as well as a group name. I think it's a lack of forward planning when the forum was first set up. The nearby rankings were "something-active" so I changed it to fit in.
It took me a while to find out why some people have ranking stars and others have stars to indicate the group they are in. Seems there is a choice in your user settings.
Profile -> Edit Profile -> Settings -> Display Group
If you set it to "None" the special stars go back to a normal rank. I have done it on mine and you can now see I'm actually a 3-silver-star user, which I personally think is better than a meaningless, static rank. I think its purpose is when you have a lot of members on a forum and want to point out admins, but because of the small user count it's not as useful as it could be.