I find myself explaining to people why they should care about Twitter quite often, so I recently wrote up a comprehensive blog post about it.

Twitter-Me This: http://www.gee.ky/blog/2008/05/twitter-me-this.html

My reasons include: Social Network, Keeping in Touch, Minutia Can Be Meaningful, Mobile Chatroom, Information On-The-Go, Privacy Shield, Accessibility, Forced Short-Form Communication, Pulse of the World, Proxy, and Brand-Monitoring.