What is it?
Here is a fun video about what Twitter is. It's more about personal use, but is still a good overview. Oh, and note how they used drawings to portray what happens on screen. Kinda clever.

How to Use It

Products for sale
Notify your "followers" about exclusive sales, promotions, coupon codes
Announce product launches, recalls

Events
If you are a band, announce "secret shows" or appearances
Announce locations, times, special guests You can reveal the date and time online but invite people to "follow" you on twitter in order to get the location. This makes your event feel exclusive.

Toot your own horn
Twit about press mentions, tv appearances, etc.
Notify followers when you have updated your blog

Other Ideas
Polls - Ask a question and post the results.
Notify followers of extended hours, a new menu, trends, etc.
Tie it into your Facebook and LinkedIn accounts for instant "status" updates.
Use it to update your website (we do this on our homepage)

PC World recommends using a character like your company mascot. It also suggests you find out when people are talking about you and make sure to respond:

\\Scan for customers. Search for your company name, products, and learn what people are saying about you. Enter your search string and even click the RSS link in the upper-right to permanently track search results. Reply to customers through Twitter. I vented once to no one--and everyone--about a bad customer experience. I was surprised to find the subject of my scorn saw my note, followed-up, and fixed my issue.\\

Are you using Twitter yet? Tell us how you use it.