The word "Listen" in Slaughterhouse-Five serves as a directing word for the reader to understand that the style and focus of the story is about to change. At the beginning of the novel, the narrator uses standard first-person past-tense, showing that the events are more-or-less concrete and understood.

All this happened, more or less. The war parts, anyway, are pretty much true. One guy I knew really was shot in Dresden for taking a teapot that wasn't his. Another guy I knew really did threaten to have his personal enemies killed by hired gunmen after the war. And so on. I've changed all the names.

When the "war part" of the story is finished, Billy Pilgrim switches to a randomly changing third/first-person, present/past-tense narration, showing that he is not certain that anything is real anymore: 

Listen: 

Billy Pilgrim has come unstuck in time.

Billy has gone to sleep a senile widower and awakened on his wedding day. He has walked through a door in 1955 and come out another one in 1941. He has gone back through that door to find himself in 1963. He has seen his birth and death many times, he says, and pays random visits to all the events in between.

He says.
(Vonnegut, Slaughterhouse-Five, Google Books)

At this point, Billy speaks of himself as if he is relating someone else's story, and as if he does not fully believe it. He starts a few other parts of the story with the same word "listen" to show that he wants the reader to see past his obvious words to the subtext underneath; Billy might be simply insane, but wants to be heard regardless. When the reader is asked to "listen," it means that the following portion of the story may not be entirely true.