Tonight I'm trying to help someone to better understand Twitter as one of the technologies that is fueling and supporting new types of conversations and interactions between people. I'm seeing the common "I don't get it" and "what could you possibly do that is useful in 140 characters?" questions.
Below is a great video by CommonCraft that does a good job of conveying the basics of the Twitter proposition. Twitter doesn't replace the other tools (e.g. blogging, email, IM, etc.), but it and micro-blogging do have a meaningful place in the conversational toolkit.
While the video is great, it leaves out one additional area of tremendous value - the power of Twitter as a means of discovering interesting new people and conversations from outside of your current sphere. I've posted a bit about this here http://bit.ly/11j30S and here http://bit.ly/XQe9k.
I hope this is helpful!