The clock in this story is symbolic of mortality. It is made of ebony, a black wood, and black is often symbolic of death. Further, the clock is housed in the seventh, westernmost room in Prince Prospero's abbey, a room of black and "blood red." Red, in this story, is also associated with death because it is the "Avatar and [...] seal" of the terrible and fatal disease raging through the kingdom. Moreover, the sun's route is frequently symbolic of a human lifespan: sunrise is birth, the sun at its zenith is midlife, and the sunset is death. The sun rises in the east and sets in the west, and the room farthest to the west is the room made up of colors associated with death. For these reasons, in part, the clock seems to be symbolic of mortality.
In addition, the clock has a fearful effect on the partygoers. When the revelers hear its chimes, and most especially the chimes at midnight, even "the giddiest grew pale" and the older members of the company "passed their hands over their brows as if in confused reverie [...]." The clock makes them nervous, as if it reminds them of the inevitable passage of time and their own limited amount of it. They have tried to escape death by coming to the abbey, but the clock serves as a reminder that they cannot live forever (and this is another reason that they avoid the room where the clock is housed).
In the end, after the Red Death has made its way through the company, "the life of the ebony clock went out with that of the last of the gay." Even the personification of the clock as possessing a life that can "[go] out" seems to confirm the idea that the clock symbolizes mortality. When everyone present is dead, it goes dead too.