The carriage in which Death and the speaker ride is a metaphor for the way in which we make our final passage to death. If you want to be literary about it you might think of Dante's Inferno where the souls are ferried by boat into hell. Or, on a more familiar level, it's pretty common for a hearse to carry a coffin to its grave. The carriage in this poem is the mode of transportation to the afterlife. We have to get where we're going somehow.