I'm not convinced it's actually that important. There's this feedback loop where the media treats Twitter as important and so celebrities and politicians (but I repeat myself) treat it as important and so on. But do real people actually care?
I think it is important because it's an imperfect but easy-to-use tool to get a quick-and-dirty sense public sentiment. (When governments realize that they'd do better to perform a MITM attack on twitter rather than shut it down, allowing them to craft whatever public perception they like, then Twitter's usefulness will drop.)
