This is an anthropological explanation.
We're fans of particular celebrities because of the way we learned the skills we needed when we lived in little hunting and gathering bands for millions of years before adopting agriculture and becoming sessile, about 10,000 years ago.
We learned the skills we needed to know by following and imitating the people in our tribe who were best at a given skill. Everyone in your tribe knew who the best hunter was; the best fisherman; the best rain shelter-builder; the best communicator; the best edible plant-finder; the best water-finder, weather-predictor, etc. etc.
There wasn't much instruction. Mostly we watched and imitated. Kids imitate naturally, without even knowing they're imitating. We get less good at it as adults, but most can still do it.
Now in this society we know consciously how it works, more or less, but our instincts still think we're hunting for food in East Africa's woodlands.
It's hard to figure out who's the best dentist, or ophthalmologist, or auto mechanic, or...
But those jobs didn't exist back in the tribal day. On the other hand, what makes celebrities outstanding is far more obvious--a beautiful singer like Jackie Evancho, a dynamic action movie actor like Tom Cruise, a clear communicator of upbeat female teen angst like Taylor Swift. Or someone whose behavior embodies the ideals of our society, like the celebrities who don't become divas but act kindly and responsibly towards others.
So our instincts kick in. We want to follow the celebrity around and pick up their skills through imitation. We can't--not without getting arrested for stalking--and their skills probably aren't the ones we need to acquire (or that are beyond our ability to acquire). But our instincts still think it's 100,000 years ago, and they're just urging to do what our instincts "understand" is best for us.
Fandom isn't very "useful." But it's very understandable.