Terry P., the joker of the two, claimed that he had had the same pillow for twelve
years. He started into a stand-up pillow talk comedy routine. While Dan provided straight lines for Terry P., Terry M. and I got serious about checking out the pillows.
It means providing the material that the comedian uses to tell the joke. Pairs of comics will often have a "straight man" who says something that enables the other one, the comic, to get the joke off. A straight man might offer a straight line like, "So, I hear your wife talks a lot" which is obviously not funny, but enables the other one to do a series of jokes about his wife.
Here's a classic straight man and comic bit. Bud Abbott, the tall guy, is the straight man. Lou Costello, the short round one, is the comic. His lines get the laughs, or his misunderstandings get the laughs.