Like our narrator, the old men on the ship have no name, and with the exception of the captain, we can't really tell them apart. Poe stresses how weird they all are: speaking in a strange language ("He muttered to himself, as did the first seaman whom I saw in the hold, some low peevish syllables of a foreign tongue" (21), and using outdated tools to navigate there way through some pretty treacherous seas.
They're all so old despite the fact that sailing needs younger, hunkier men to really work. Are they ghosts on a haunted ship? Are they off on one last adventure? How long have they been sailing anyway? We never get an answer to who they are or where they come from, and the mystery makes the story all the much spookier. The narrator briefly mentions a commission from an unknown king—"he pored with a fiery unquiet eye over a paper which I took to be a commission, and which, at all events, bore the signature of a monarch" (21)—but that's the only sign of where they might come from. Shmoop's theory? Zombie sailors.
The old men also display an eagerness for what's coming that the narrator doesn't share. They're not afraid of the whirlpool. In fact, they're looking forward to taking the plunge. Now this is just plain crazy: "There is upon their countenances an expression more of the eagerness of hope than of the apathy of despair" (26).
Again, we never know why. They could be excited about the notion of an adventure. Hey, the whirlpool could lead right through the center of the planet and pop them out at the North Pole (and how cool would that be?) On the other hand, they may simply be crazy and head to the whirlpool as a spectacular way of dying… or ending their eternal suffering if they're some kind of ghosts.
Whatever the reason, it's clear that the whirlpool holds great importance to them. It's the primary focus of their characters and—considering their age—might be something they've been trying to reach for quite a long time. Their enthusiasm suggests that they're finally coming to the end of their quest… and the narrator just gets to come along for the ride. (Lucky him.)