Twitter shows trending topics, but it's for the entire user base. You can only see what everyone on Twitter is talking about at any given time. Trendsmap, on the other hand, shows trending topics by location. See what's trending in any part of the world in real-time.
The more popular a topic is, the larger it appears on the map. Click on a topic, and read the tweets that are coming in. For example, I'm looking at 'protest' right now in Pittsburgh. It looks like there's a protest happening at the University of Pittsburgh. There are also thumbnails for YouTube videos and Flickr photos.
Zoom into your region, and it gets much more interesting:
That is, if you live somewhere where something is going on. Otherwise, maybe not so much: