Twitter is, I think, one of the more important developments of the last 10 years of the internet. Seriously. Because it is, at its heart, purpose-less. It exists less as a thing-unto-itself, like Facebook and MySpace and all those other networking sites you've used, and simply as a communications medium, a means to other ends.
It's like email in that respect. The analogy is actually quite fitting: both email and twitter were based off of an already-existing communication model: email on the postal service, and twitter on text messages. Both then took that existing model and opened it up: email allowed for instantaneous communication as well as multiple recipients, among other innovations; twitter moved the text message from the control of the carrier and phone-to-phone and replaced it with a centralized, relatively open platform for development.
This open model is the most important thing. When twitter was created, @biz and @ev and @jack didn't have a specific plan in mind for its use -- the unspoken assumption was that users would best be able to figure out the best uses. Users developed the @ syntax for replies, and thousands of independent developers flocked to the open API, building amazing tools around the system. No one development team could replicate all the various permutations that these developers have built around the system.
The Onion parodied this seeming lack of direction with the headline "Twitter Creator On Iran: 'I Never Intended For Twitter To Be Useful'". I think it's truer than they might have known, but that lack of purpose means that twitter is a chameleon, with every user using it in a different way, each to his or her best interests. It's the biggest revolution in how we communicate since email.
Loath as I generally am to link to something like TechCrunch, they actually ran an article recently that extends back Twitter's lineage. SMS text messages, it turns out, were based on the average length of the message someone could send on the back of a postcard. So, by analogy, if letters begot the modern email message, Twitter is simply the new version of the hasty postcard. The deeper message of that article, however -- that email and traditional story structure is somehow 'inferior' to the short-form Twitter message -- is pretty well disproved by the story itself. The comments, while rude, abrasive, and snippy, make this point:
If what you say is so true, then why couldn’t you do it in 140 char? -- #comment-2836606
Twitter isn't a replacement for anything. It's an extension, and it's really good at short messages to anyone who cares to listen. It's not the future of communications.