Wired has an article on Twitter by Clive Thompson which is spot on:
Twitter and other constant-contact media create social proprioception. They give a group of people a sense of itself, making possible weird, fascinating feats of coordination.
I've several friends using Twitter who I'd love to see more often. I'm not going to manage that, but at least when I do see them now the conversation starts in a much more interesting place. We both have a sense of whether things have been fun or crap lately. Since the Twitter messages are so short, they sometimes only just make sense after chatting about it.
Twitter's great, and I expect we'll see more of this ambient presence in other spheres before long.