The train seems to symbolize life and moving through the stages of life. Literally, the boy is going from one parent to the other, but symbolically, it represents moving through life. He is moving from pre-adolescence into adolescence and beyond, I think, into adulthood at the end, as the father mentions his moving out of sight.
The train is a symbol for the process of life that carries the son inevitably into adolescence and adulthood, and away from his father. The train will take him to unexplored areas of his young life, not only geographically, but intellectually and sexually as well.
The whole poem is about this, whether the train is directly mentioned or not, but you can see the symbolism of the train most directly in these lines:
the huge train waits, crowding the station
with aftermath and longing
and all we’ve never said
to one another. He shoulders
his black dufflebag and shifts
from foot to foot, restless to be off,