Apperently, the upside of it is that it allows you to talk to certain people more easily. I wouldn't say 'celebrities', but still people that are considered somewhat famous by a wide group of people. Twitter allows you to immediately see what cool thing they did and respond to their questions, or ask them things personally and actually get a response.
Though, this is just from what appears to be the case in certain... cases. There are also people that just share any and each unimportant thing that happens in their life, hoping to draw attention because they don't get enough in real life. This leads to such things as '****ting now'. Sometimes they will try to interact with their followers, asking 'what milkshake should I take?!', while waiting in the drive-through for a response, and everybody else is honking their car because somebody thinks it's important to get attention.
Oh, and 'twitter' comes from the 'tweet' that birds make. You 'tweet' messages like a bird, so it's called twitter.