Facebook explains "The Graph" in their developer documentation:
Now that you've seen how actions and objects interact with people and your app, it's worth pointing out that this is why we call this a Graph. In computer science, a graph is a set of objects that are interconnected. When you create a story on Facebook, you're not just posting text for someone to read. You're also creating a set of structured relationships, as well. Your app, the person using your app and the article they like are all now connected. This is why we call it a graph. You're not just telling stories, you're also creating a structured history of the things that people have done in the world.