Nice question! It is a symbol in several ways, and of several things. First and most simply, it indicates how quiet the room is. In that instance, it is barely a symbol, but rather just a sign. However, it becomes a symbol, representing more than just the quietness or Emily's mode of dress, when put into context. The silence comes from the respect the town has for her, and so the very quiet is symbolic. The watch is on a gold chain, just as Emily is "chained" by her father's wealth. It, and the time it counts off, moves on, even when no one can see it passing; this will be symbolic of the rest of story to come, especially of how time passes regarding the town and Emily's beau. This passage of time is at the end of the chain, just as things are at the end of their ropes (metaphorically). When time passes, Miss Emily ends up at the end of her rope.

To further add to the symbolism, look at the other instances of gold in that area of the story—the tarnished can head, the tarnished gilt easel. Golden (precious) things are tainted in this house.

Greg

In "A Rose for Emily," what is the significance of Emily's watch?

Early in the story "A Rose for Emily," the narrators describe a "called special meeting of the Board of Aldermen who then visit Miss Emily; before a Tarnished gilt easel ....[and] a crayon protrait of Miss Emily's father, stands Emily herself.  She is a small woman dressed in black, "with a thin gold chain descending to her waist and vanishing into her belt."  She looks "bloated."  As she stands in the door, the other people can hear the muted ticking of "an invisible watch at the end of the gold chain."

Since this description is juxtaposed with the portrait of Miss Emily's father, who exerted tremendous influence upon Emily, the reader may conjecture that the watch and its long chain have belonged to the now-deceased Mr. Grierson.  Invisible, but still ticking, the watch symbolizes Emily's father's post mortem  control of his daughter who wears his watch, funereal color with bloated flesh--much like that of a dead person, too--in order to retain his memory and feel the influence under which she lived her life.