I've never "got" Twitter, how do you use it and why do you enjoy it?

I've been on Twitter for awhile now. I know it's feature set, I follow people other people follow, I use nice Twitter clients--but I just don't enjoy it. It just feels like a bastardized, less precise RSS feed or Facebook with a news feed full of strangers. What I am missing here?

My Twitter handle is @ineedmyidback (got hacked, couldn't convince twitter to give me my original username back) if anyone wants to check out what I'm doing and tell me what's missing.