They inadvertently solved the need of microblogging. No need to maintain blogs; no need to write long posts. Just a simple, short way to keep people informed with what you are doing. But that's not what made them big either.
What made them big is celebrities took to it and used it as their main form of communication with their fans. That's why I made an account a few years back and I'd venture to say over half of the active users did the exact same. Twitter has since evolved past that, at least for me, but it was definitely the initial reason for the boom. Would they have been successful without that? Probably not.
So is Twitter a good idea? I don't know. I really don't know.