I also had that feeling initially, so the first time I had a profile there, I deleted it after a day, thinking, "What's the point?"
What Twitter is used for differs from person to person. Some people call it microblogging, but I wouldn't say it's that. For me it's a bit like an asynchronous chatroom. I go there mainly to socialise. I have a fair number of Aspie and ADHD friends there too.
For some people it's about networking for business; for some it's marketing. I have a different Twitter profile for my business, where I use my real name and post announcements of events which they can attend.
WrongPlanet.net also has a profile and the headlines of the new threads here appear on Twitter. I often click on those links at Twitter when it looks like something new and interesting. I suppose that functions something like an RSS feed does for a feed reader.
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When I must wait in a queue, I dance. Classified as an aspie with ADHD on 31 March 2009 at the age of 43.