I don't use Twitter nearly as much as I did a year or two ago, but I still check in daily and post something. I like it better than Facebook wall posts, and since I have my account set to "private," only those people who are following me can read my updates. I just don't like broadcasting to the entire world everything I post. I like the fact that I can limit it to a select few. I also like the fact that I can cross-post my Blip.fm posts on it.
The key to Twitter is finding people you know or like and follow them (and getting some of them to follow you back). That's what makes it interesting, fun and worthwhile. I hear so many people who try it out say they don't like it or don't get it, but when I look at their profile they're not following anyone, or the people they're following don't use it either. Well, duh!
For bands, it's just another way you can post what's going on with the band... recording, going to play a gig out of town, playing a show in town, etc. It's a great way to keep your fans updated on what's happening with the band.