I kinda get it, and I kinda don’t. I spend a lot of my free time researching random things, and often it’s the life of a celebrity. I’ll go dig up all their movies/albums, pester the library for books – bonus points if the obscure book is something they’ve written, and JACKPOT! if they’ve actually got a readable autobiography – and go scouting around online for interviews, particularly if they’re recent enough to have been on video. But I really only do it if the celebrity in question is someone I’d also be interested in if I knew them personally. I run a profile on them because they’re intriguing; I just know they exist because they’ve been in a bunch of movies. In that case, I pay attention to minutia the same as I would someone I get to hang around in person. Details can tell you more than you’d think.
On the other hand, I don’t get why Random Celebrity X getting coffee is so fascinating to most people that nationally-distributed magazines will pay money for a picture of it. Hoovering up gossip about anyone famous that happens to cross your radar is essentially paying attention to something strictly because other people are paying attention to it, which isn’t usually enough of a reason for me to care. Paparazzi photos also give me the willies for reasons I can’t quite explain, and I refuse to use them when I do my researching bit – I stick strictly to things the celebrity intended to make public. (Or, if I’m poking into true crime stuff, what the investigation made public.) So I can’t give you the general reason for it, on account of I apparently squick easily when confronted with invasions of privacy, and I avoid them.
I suspect that a lot of it is either schadenfreude or an effort to identify with people we see as living on a different plane of existence. Look, we both get Starbucks in the morning! or Hey, at least my life isn’t a giant public drug disaster! I tend to pick different stuff to identify with, though, so the whole bonding-through-coffee thing doesn’t work well for me.