The setting in this story is incredibly important. It involves the seven rooms all of different hues, but also the clock. The clock itself is a symbol in this story and points to one of its major themes. To understand symbolism you must look at how the object is used by the author. In this case, we examine the characters' reaction to the clock.
Remember that the characters are hiding from the pestilence of the "Red Death". "No pestilence had been so fatal, or so hideous." In a sense, they were hiding from death and mortality. The characters react to the clock by stopping everything they are doing. The orchestra stops playing and "the waltzers perforce ceased their evolutions . . . it was observed that the giddiest grew pale". This is because the clock is an instrument of time and thus symbolizes mortality. The characters hear the chimes of this clock and are reminded of how, no matter where they hide, they will all eventually die.