The Matt Damon thing is a long running gag on the show. At the end of every show, Kimmel says something like "Apologies to Matt Damon, we ran out of time" (effectively bumping him from the show). When Matt Damon was actually scheduled to be a guest on the show, he was given a long rambling introduction, and then as soon as he sat down, Kimmel apologised and the show ended.
Which led to this:
http://www.youtube.com/watch?v=eSfoF6MhgLA
Which in turn led to this:
http://www.youtube.com/watch?v=TwIyLHsk2h4
Which led to this:
http://www.youtube.com/watch?v=eSfoF6MhgLA
Which in turn led to this:
http://www.youtube.com/watch?v=TwIyLHsk2h4
