Google suggest using the tool to identify how the news broke, or see what people were saying about a specific popular issue. Anyone watching the Guergis/Jaffer affair last week would probably want to check out #bustyhookers (I'm not just being gratuitous, there's a really interesting story behind it for those who weren't following).
I can see it being used for public relations metric purposes, but also discovery for future online defamation cases. Some have expressed concerns about the utility of indexing Tweets, and offer solutions to delete them. Specifically, some are worried about being targeted by advertisers, or excess scrutiny of historic Tweets used to chill speech.
Google is rolling out the features over the next few days, but you can test it out on a special link demonstrating trends for Obama.