Meh, twitter makes sense to me when you understand two things:
1) It's fully public, and everything you're a fan of uses it.
This makes it fantastic for building a feed of stuff you follow in tiny, tidy, bite-sized messages where one overactive wall-of-text can't slow you down as you drink from the firehose of info.
2) It came out of SMS. That means it keeps the limits of SMS, like short messages and usernames and whatnot. Imho they should break out of this box a bit - move tags and people out of the message body and swap names into the UI.