For me, stars are a rough measure of traction. If I can get a project above 1000 or so, my project begins to take on a life of its own, and I can concentrate less on marketing and awareness.
I would say that stars are mostly a measure of interest/coolness. The difference to actual people using it can be absurd. The biggest project I maintained had 5k+ stars (which it got by landing on the HN frontpage a few times), but the actual amount of people that tried to use it is in the 10-20 range. On the flipside one of my other projects has a lot more users than it has stars.
With all that, stars have basically lost all meaning to me if I'm looking at it as a project outsider, and only have limited meaning as a maintainer.
Thus I always felt a little weird about the hype around the number of stars.