"The cattle are lowing,
The Baby awakes.
But the little Lord Jesus
No crying He makes"
These four lines appear in one of the most famous Christmas carols ever, "Away in a Manger." (Listen to it here!) Although we could speculate endlessly about why Vonnegut picks this particular Christmas carol for his epigraph, the author makes the reader's job a little easier by giving us a reason. In Chapter 9, Section 20, the narrator comments that main character Billy Pilgrim always cries silently when he weeps after the war. He weeps very little, even though he has "seen a lot of things to cry about" (9.21.2). In other words, like the baby Jesus, "no crying he makes." For more on Billy's character, check out his "Character Analysis."
Vonnegut does this kind of thing all the time in Slaughterhouse-Five: making a reference to a Christmas carol or a novel or a history book. And he'll also include the reasons why he does so. He just doesn't always include the explanation next to the reference itself.
Slaughterhouse-Five is like a wordy version of a scavenger hunt, where you have to search through the whole book to find the clues you're looking for. The epigraph appears just before the first page of the book, but we only get direct comments on what it means in the second-to-last chapter. For more on the circular structure of the book, check out "What's Up With the Ending?"