It's generally useful for friends or acquaitances. For example, I tend to twit when I just want to say something that I don't think warrants a blogpost. Short questions, shouts, messages to friends that might be listening, small rants.
Generally it helps take out some load off my mind :)
If you have Firefox, use the TwitterFox add-on, it's wonderful and makes it soooo easy and keeps it out of the way. <3
As for the point of twitter, there really isn't a point. It's just a cute little thing that pops up and tells you about the people you're interested in. It's also great for linking to new posts, or when you want to link friends to random little things you find.
I literally JUST signed up like 10 minutes ago, saw a segment about it on DiggNation podcast. Guess it will be cool for quick updates for friends and family on how things are..? Still new to the usage.