The Facebook Wall is probably the most famous example of an activity stream, but just about any application could generate a stream of information in this format. Using a common format for activity streams could enable applications to communicate with one another, and presents new opportunities for information aggregation.
In our interview with him earlier this year, developer Max Ogden explained the appeal of Activity Streams:
ActivityStreams is implementing what is called "actor-verb-object" logic to represent social streams. So if you look at the front page of Github, of Twitter, of Facebook or any other social network (or feed) you can extract actor verb object triples such as "Max pushed a new piece of functionality to his project on github" or "Tyler posted 'hello max' to your wall" or "Klint uploaded a photo of his cat to icanhazcheezburger."
Activity Streams is already in use at BBC, Gowalla, Socialcast and at several other companies. We really hope to see this take off in a number of applications, since it will make creating aggregated activity streams much easier. We've discussed how something like this could be used in enterprise applications here.