At the moment, you can go to Twitter's site or use the app on your mobile phone to tag your location along with your tweet. You can either pick from an existing location, or enter a new one; the list of place names is sure to blossom quickly. Then anyone who reads your tweet, including you, can click on that location to see recent tweets also linked to that location. Twitter is pegging the release to the World Cup: see who else is at the stadium, or, more realistically, at a particular sports bar or venue.
Interestingly, Twitter's also partnering with existing location-based startups Foursquare and Gowalla. If you click on a location that's associated with checkins from members of either one of those services, you'll see those updates in your Twitter stream as well. This is great for Foursquare and Gowalla--it opens them up to a huge field of Twitter users in a much more integrated way.
Twitter's releasing an API as well, so developers will be able to integrate Twitter Places into their third-party apps. Location is also supported in more browsers than before--Safari and Internet Explorer join Chrome and Firefox in compatibility. Going along with that, Twitter's own iPhone, Android, and BlackBerry apps will be getting Places integration at some point in the near future.