In my opinion Twitter is 10% useful, 90% hype. How is it useful? The argument that I've heard is that in a corporate team environment, Twitter is more appropriate for short messages than is email. That's the only one that kinda makes sense to me.
Twitter as a real-time search tool doesn't make sense to me. Anyone who has used Twitter for a day or two knows that the "tweets" are mostly garbage. It's more difficult to get context from short messages, so more difficult to sort the garbage from the nugget of information you are looking for.
I've also tried to use it for promotion. Compared to Digg, or Reddit, it doesn't drive traffic nearly as effectively. For that to work, I imagine I'd need real followers who hang on my every tweet, rather than just other people trying to promote their websites. Unfortunately everyone I know in real life thinks Twitter is as stupid as I do.
So why is Twitter the next big thing, and why is everyone talking about it? Short answers, it isn't the next big thing, and people are talking about it because they are being paid to talk about it. So if you have heard about Twitter, or actually tried Twitter and are wondering "what's the point?" you're not alone.