Twitter is not new to the breaking news segment, and most of the recent disasters have first been widely reported on Twitter. These are just part of the discussions which form part of Trending topics on twitter (see Top Trending Topics for 2009 on Twitter).
The trending for cities/countries is basically based on the new Trend API which twitter had announced. With the Help of the Trend API, users from different cities or countries would be able to view what is trending in their local areas. According, to TechCrunch, Twitter has started to rollout the Local Trends to few users.
Here are some screenshots of the Local Trends which will be gradually rolled out to everyone, courtesy TechCrunch.
This move by Twitter is definitely a good one, as local topics that have some value usually do not trend globally and users from a particular city or country would benefit more to know what is happening near them, rather than something that is happening across seven seas.
However, from the screenshots available, Twitter will continue maintaining the global trending topics, whilst offering users an option to view topics trending in their country or city. Right now there is not much information available about the countries and cities which are supported, however, you can expect a official announcement to come forth soon.