The role of the smell in "A Rose for Emily" is that it foreshadows the final realization that Homer Barron's body has been decomposing inside Emily's house for years.
Because Faulkner's narration isn't a chronological ordering of events, the foreshadowing that readers get is served up in randomly ordered pieces. The smell is actually the first major hint to readers that something isn't quite right about Emily and her house. It isn't just that the house has a small unpleasant smell about it. The smell must be something terrible and quite strong because several members of the town file complaints.
The next day he received two more complaints, one from a man who came in diffident deprecation. "We really must do something about it, Judge. I'd be the last one in the world to bother Miss Emily, but we've got to do something."
Judge Stevens weakly tries to defend Emily by saying that the smell is probably a dead rat. This detail further alerts readers to something ominous. A dead rat smells up a room in a house. It doesn't smell up half of a city block. Something larger must be decomposing in Emily's house.
As the story continues, Faulkner drops three more key pieces of foreshadowing. The first is that Emily is very reluctant to give up the dead body of her father. The only reason she does do it is because the people of the town actually know for sure that he is dead. The next major piece of foreshadowing is that Emily buys arsenic. Finally, readers are told that Homer essentially disappears without a trace.
And, as we had expected all along, within three days Homer Barron was back in town. A neighbor saw the Negro man admit him at the kitchen door at dusk one evening.
And that was the last we saw of Homer Barron.
At the story's final conclusion, readers realize that Emily killed Homer with the arsenic and kept the decomposing body in her bedroom. It's then that the reader's suspicions about the smell are confirmed.
The role of the smell that emanates from Emily's home after the disappearance of Homer Barron has two functions. The first is to alert the reader that Emily has probably killed Homer and the smell is Homer's rotting body. The "smell incident" also tells the reader a lot about the Southern society Emily inhabits. The townspeople have no idea what the smell could be or, at least they won't admit it to themselves. In addition, they refuse to confront Emily directly because she comes from such a distinguished family. Judge Stevens, the town’s mayor, won't do anything about it for fear of offending Emily (‘‘Dammit, sir … will you accuse a lady to her face of smelling bad?’’). The ladies accuse Tobe, Emily's manservant, of poor housekeeping. Four men finally sneak up to Emily's home at midnight and sprinkle lime around it. When they are done, they see that ‘‘a window that had been dark was lighted and Miss Emily sat in it, the light behind her, and her upright torso motionless as that of an idol.” This "idol" is probably Homer's body, not Emily. But, as this incident has shown, the men are blinded by tradition and can't see the obvious even though it is right in front of their eyes.