In the story, a huge black clock stands against the westernmost wall of the last room in Prince Prospero's hall. The last room is shrouded in black velvet tapestries, and its window panes are painted red; this is unusual because the windows of all the other rooms are painted the same color as the walls. However, this last room seems to represent human mortality and death's inevitability as its colors are associated with the mystery of death and blood, it is the final room of the seven rooms and death is our eventual finality, and it is the westernmost room (and the sun sets in the west, as the actual death of day as well as a symbol of death itself).
Clocks are often symbols of mortality as well, representing the unstoppable passage of time, and the fact that the clock is black (symbolic of death) and that the revelers stay away from the final room and fear the chimes of the clock -- especially when it strikes midnight (the death of day) -- seems to confirm the fact that the clock symbolizes mortality. Likewise, Prince Prospero's death in this room gives further strength to this interpretation.