For me, I don't think it's an issue of who's a geek and who's not, it's more "who's going to leave their AIM or ICQ protocols to use something on the web that does the exact same thing?".
a) Past statuses get archived. Each of them gets a permalink. You get RSS on them. There's a huge difference between just seeing what someone's doing right now, and being able to see a concise summary of their day or days laid out before you.
b) You can access it via mobile phones.
c) It is a social network. You can discover interesting people by clicking around.
d) You can follow others. This one is so huge I'm certain I still haven't grasped all of its implications. Twitter is a social network built on a single simple one-way connection, and already there's more value flowing through it than through facebook.
When I go to facebook I get spammed and poked and bitten and humped and god knows what else. Facebook is made for senders. When I go to twitter I can get a sense of what my close friends and family are up to, no matter where on earth they are, so that when I do open up my IM window to chat with them I don't have to start with the tedious "how was your day?" I have prebuilt objects to begin a conversation with. Twitter is built for recipients.
twitter scales more at the edges.
Forget mode, protocols, technology. I can be mobile with a phone, send a message not only to another phone but as data that can be further processed by machine or other people.
Longer text is better for some writers - they don't have to work to fit in their message. But it's better for all readers - they can come read their twitters knowing no single entry will swamp it.