This is Paul Simon and Steve Martin performing a sort of Christmas monologue. Reportedly the track comes from a "Saturday Night Live" rehearsal, but never made it to air for some reason.
For our friends in the Home Nations, "Saturday Night Live" (or simply "SNL") is a long-running television programme that has served as the starting point for most of America's comedy catchphrases. Americans always struggle with the fact that SNL doesn't exist in Britain. We'll say something like, "It was better than 'Cats,'" and you will just sit there and stare at us in that way you always do.
One thing I find interesting is that I can hear my own comedic timing in this. That's not surprising, I guess -- when I was a boy, I listened to Steve Martin records over and over and over (perhaps a questionable decision on my parents' part, but there you go).
My favourite part comes at 03:20.