It is some measure of popularity/maintenance. In choosing something to use, I would first check the activity (as a proxy to rate of bugfixes, for one), and second I will check the number of stars (as a proxy to how many people are watching/using this).

If there are more stars, I would assume that if the owner of the repo dropped off the face of the earth, it's more likely that a new maintainer would step up.

From my personal observation, those two go together and I usually don't take them in isolation. One may be able to game the stars, but they won't be able to game activity (issues, commits, etc.), I'm hoping at least not in a meaningful manner.