It's not a matter of "sense". If I could recount the number of times that people told me Facebook was irrelevant because "email" existed and I could use it for the same reason I use Facebook (to stay in contact with people), we'd be here all day. The fact is, I've connected with lots of people in my industry and area with Twitter, and lots of them if not all have become valuable assets in what I do.
I wouldn't be so crass to quickly dismiss it as THE method of communicating. The marketplace wont let that happen, and social dynamics wont let that happen; and in my opinion I think that is another crucial thing people fail to realize when stacking Twitter up against traditional communication: the social dynamics of how useful it can be.
But again, there's no archetype for how you use this type of service, or any service. It just so happened I was online at the moment, I knew he was online (by virtue of the fact that he had posted a tweet not even 10 minutes earlier) so I alerted him to where I was.
It's really that simple.
Furthermore, it's just a good way to keep track of what you need to know from people. Not everyone tells you useful information, but not every author who has a book published is worth reading either. It's a different experience from everyone and that's the beauty of the Internet. There are no archetypes for how you use it