All aboard, Shmoopers. You may have noticed that trains are important in this story. They take Paul from place to place, and, well, you know what happens at the end. (If you don't, check out "What's Up With the Ending?").
So here's our thought: Trains are (1) a symbol of the mobility that Paul lacks, and (2) a runaway metaphor about the trajectory of Paul's life (and the story's plot). Want some proof?
(1) Trains cut through the snowy landscape, linking Pittsburgh and New York City. They're a symbol to Paul of the possibility that he could someday leave his dreary life and make it in the big city.
But they're also a symbol of what he can't have. When he takes the night train to New York with his stolen stash, he rides a day car—i.e., coach—rather than a cushy, business-class Pullman car because he's "ashamed, dressed as he was" (2.2). In other words, he can't even go where he wants to on a train.
In a way, you could say that the train is even responsible for his death—not because it actually kills him, although, duh, it does—but because it emphasizes that he'll never be able to live the way he wants to. Like cars did for Americans in the 1950s, trains in the nineteenth century often symbolized the mobility of the modern world. People could overcome their circumstances and change their fate on a train car. But not Paul. Realizing that he's stuck seems to be a final straw for him.
(2) Moving up and out an analytical level, trains also symbolize the inevitability of Paul's fate. Check out the way the last train comes: Paul wakes from his chilly nap when he hears the "sound of an approaching train" (2.63). In other words, he wakes up out to realize that there's no way out. Just like a train, his life has been barreling toward this conclusion.
And so, we realize, has the plot. Paul wouldn't have survived if he'd just worked harder at school, or if his dad has just let him keep that usher job, or if he'd just hung on a few more years until he got to college. This is the only end way the story could ever have ended. Uplifting, right?