The Tralfamadorians are the aliens who bring Billy to their planet to exhibit him in a zoo. They also kidnap a twenty-year-old actress/porn star named Montana Wildhack so that the two can mate. The Tralfamadorians are green and shaped like toilet plungers, with hands at the end of their long, stick-like bodies.
In many ways, the Tralfamadorians are subtly compared to the Germans. The first thing the Germans do when Billy arrives at their prison camp is to make him take off his clothes, which is also the first thing the Tralfamadorians do when Billy arrives on their planet. When a German prison guard punches an American in the face and the American asks why, the German answers, "Vy you? Vy anybody?" (5.9.4). Similarly, the Tralfamadorians refuse to consider the question "why" they abducted Billy: they say, "There is no why" (4.7.6).
But most important, the Tralfamadorians, like the Germans, totally remove Billy's choices: they take him captive and there is nothing Billy can do about it. He is forced to live (he believes) in a geodesic dome on Tralfamadore just as he is forced to live in a slaughterhouse in Dresden.
The lessons the Tralfamadorians teach Billy about time (about which, see Billy's "Character Analysis") are kind of a mixed blessing. It comforts Billy to think that time is totally predetermined and unchangeable and there is no free will. This Tralfamadorian faith in the total pointlessness of trying to change anything makes Billy feel like everything he has gone through, no matter how awful, could not have gone any other way.
At the same time, we have to wonder if it isn't kind of messed up that Billy's idea of Tralfamadorian philosophy frees him from taking any blame or responsibility for his own actions. Billy embraces the thinking of Tralfamadore because it absolves him from even trying to change the way things are. He doesn't prevent his son from going to war, he doesn't attempt to remind people of the bombing of Dresden – nothing. What Billy actively chooses to do is to soothe the world with the news of Tralfamadore – to tell the world that it's OK that he has suffered horribly and will die eventually, when suffering should never be OK.
The narrator of the story resolves that he has to write about Dresden and the war, even if trying to stop war may as well be like trying to stop glaciers (1.2.12). In a sense, maybe the act of writing Slaughterhouse-Five is a way of writing against the powerlessness and sorrow that World War II, the Germans, the Tralfamadorians, and even death itself seem to inspire in him. For more on this topic, see our theme on "Fate and Free Will."