Factery is a search API with a twist. Instead of links, it returns facts. Actually, it returns links, too. But the real interesting stuff is that it extracts the sentence or two that best answers a user's search.
Another way Factery is different is that you decide the sources to use. You can search Twitter, Digg, or a standard search engine. All you need are pages containing a list of links and Factery does the rest.
At the heart of Factery's technology is FactRank, which CNET describes well:
FactRank goes through each Web page or source (in whatever index it's searching from) finding semantic tip-offs like declarative sentences. It then cross references each of those against one another, surfacing some of the most relevant ones to the top, as well as factoring in the order of how they appeared. What the user then gets is a tidy list of statements, each of which is sourced and given a level of relevancy based on their appearances in all of the indexed source pages combined.
Factery is a rare API in that the API is the service. It's not an add-on, where you can just build off of their data. Factery is not a destination--it's sole purpose is to be incorporated into your applications.