You can't really understand Twitter unless you actually do it (which might explain why I don't really understand Twitter.)
The benefit of Twitter is "social proprioception":
When I see that my friend Misha is "waiting at Genius Bar to send my MacBook to the shop," that's not much information. But when I get such granular updates every day for a month, I know a lot more about her. And when my four closest friends and worldmates send me dozens of updates a week for five months, I begin to develop an almost telepathic awareness of the people most important to me.
It's like proprioception, your body's ability to know where your limbs are. That subliminal sense of orientation is crucial for coordination: It keeps you from accidentally bumping into objects, and it makes possible amazing feats of balance and dexterity.
Twitter and other constant-contact media create social proprioception. They give a group of people a sense of itself, making possible weird, fascinating feats of coordination."
Sound interesting? It should have more :-)