I've played around with the Twitter Search a little bit. Basically it's just a way to keep tabs on keywords that people are tweeting about. You can see it in action here in the lower right of the mojoPortal Community page. Joe has it set up to watch for tweets about mojoPortal.

One thing I was disappointed in (and this isn't a mojoPortal issue) is that the Twitter search ability is lacking. For instance, you can't construct a query to return tweets that mention "New York", but without the phrase "I'm at".  Because, really, who wants to see tweets saying "I'm at Monk's Diner in New York City!" Wow, good for you!