Common Craft has put together a great video on what is Twitter and why it might be useful to you. I began using Twitter a few months ago.
One thing I like about Twitter is that it is easy to embed into other sites. For example, my Facebook status can be changed by Twitter. Also, there is box on the blog site with my latest Twitter post.
I have thought that Twitter or a variation would be useful inside the firm. I could keep my assistant up to date on where I am and how to get a hold of me (if I am reachable).
If you like this video you should also see Common Craft's Plain English videos on RSS, Wikis, Blogs, Social Networking and Social Bookmarking