My6sense is a mobile app that basically gets to know what you like and what's important to you, after which it organizes and filters your different web content -- RSS feeds, Twitter messages, Facebook updates -- based on your preferences.
The app gets more and more accurate the more that you use it, because it can take advantage of monitoring how long you spend on certain articles, what type of authors or content you gravitate toward on a certain source, and what type of information you find most useful.
My6sense already has an iPhone app as well as a Twitter tool called myTweetsense; the Attention API is the latest addition to the my6sense stable of tools, allowing publishers integrate their own feeds into my6sense, so that users can get personalized content from that source. This data can also be integrated into other mobile applications and also with other services.
A possible use case would work like this: A user could choose to subscribe to a my6sense stream of Mashable.com and in turn would get served the content that they most want to see in order of importance and interest. So instead of having to go through all the articles in an RSS feed, the most important stuff will bubble up to the top.