Twitter does, however, provide me with insights into the people I know (business or otherwise) and keeps me on the edge with developments in several communities I'm involved with. For example, I'm a Ruby guy, and so I follow a lot of Rubyists.. you can bet I'm pretty clued in to brand new Ruby libraries, etc, as they come out (or even just in a very quiet personal beta).
Explaining Twitter is next to impossible. Unless you've been using it in anger for a few months, you don't have a clue what it is, but then suddenly.. one day you do.
Yes, it is. There's a reason why Knuth answers regular mail as a batch process (once every few months), for example. A common productivity tip is to limit yourself to checking email only a few times a day. The productivity harm caused be frequent context switching has been well-documented, especially if you're doing something context-intensive like programming.
But you don't have to deal with e-mail as a dribble, as you say. I deal with e-mail as a batch process, just several times a day instead of once every few months. Ditto for Twitter and the like.
Not sure I explained that well, but I think you can get my meaning.
Twitter can be a distraction (and I let it be more than I should), but like anything else it can be managed.
On one end of the spectrum, I follow people who have similar interests as me (Ruby, Rails, Clojure, Arduino, Macs, etc). Lots of them are well-known in their various niche communities. Yes, you do get some degree of "drinking coffe" and "walking the dog" type of notifications, but a lot more "hey, this piece of software is cool", and "I just released this new library" messages. The signal to noise ratio is really pretty good, assuming you are choosy about who you follow. If you follow interesting people, they will help you find interesting things. I wrote about this a little bit, particularly about how I read RSS feeds much less now because of Twitter: http://larrywright.me/blog/articles/209-the-coming-decline-o...
On the other end of the spectrum, I do follow people that I know personally, or that live in the same town (it's small). What I get from these people is different. It's more akin to meeting down at the local coffee shop and catching up. There's value in this as well.
It's very easy to dismiss Twitter unless you look closely. You're right, in a sense: I don't care what a random person is doing right now. But that's not really what Twitter is about, and until you use it for a bit, that's hard to understand.
If you want to try it, find some people whose blogs you enjoy reading, and follow them for a bit on Twitter. I think you'll be surprised at what you find.
If you do, you can find me at http://twitter.com/larrywright