Twitter is what you might call "micro-blogging". You are allowed 140 characters per post, so you tend to do lots of short posts. I'm checking it out to see what can be done with it.
I'm thinking I may be able to use it at work. If everyone in my team keeps Twitter updated with what they are doing, and we are all "friends" on Twitter then we will always know what each person is up to. E.g., "Where is Joe?" Look at his Twitter - he is at lunch or he's in a meeting or whatever. I can see that it could be useful for such things. I'm not really all that clear on what else it could be used for, but we'll see.
Anyway, while I'm checking it out, I've put the feed from my Twitter over on the right at the top of the page. So check out my Twittering and tell me what you think.