Compositing is the process of combining two (or more) images or parts of an image together to create one complete new image. That can be anything from a split-screen effect to clone someone, inserting 3d models into live action, adding digital blood and explosions, etc..
Is there something in particular you're after, or are you talking more about an overall look (in which case you'd be looking more for color correction than compositing) ?
well I was thinking of compositing with FCP, so I had compositing solids and gradients over my video footage in mind, but I see how color correction would be more of what I was thinking as well. I'm going to check out those after effects tutorials though and see what you are talking about. I definitely wasn't thinking about 3D images, just ways to enhance the look of some rather drab footage I have.