In addition to the previous post,
Keep in mind that Faulkner used phrases such as "an eyesore of all eyesores", and "a reminder of the past" to refer to both Emily's house and Emily herself as a picture of her former self. It is as if Faulkner perpetuated the description of the town and of Emily by appealing to the senses of nostalgia, staleness, and by almost making us sneeze with the "dust of the past" still clinging on to the main character, her home, and her life.
However, it is almost universally understood that Faulkner, as a Southern Gothic, is meant to provide these details to instill in the reader that same feeling of sadness and to foreshadow more of what is to come in Emily's life.
The dominant aspect of setting in Faulkner's "A Rose for Emily" is the post-Civil War South. The dominant aspect of character is Emily's resistance to change.
Emily's family was once Southern aristocracy, in a sense. In the past, her family was wealthy and were leaders in the community. Presumably, when the economy in the South declined following the Civil War, Emily's family lost its fortune and place in society.
Emily, however, refuses to let go and adjust. She refuses any change.
The setting, then, involves forceful change in the South. But Emily's personality and character make her resistant to change. You can see how setting and character reinforce each other in the story.
If you break these broad aspects down a bit, Emily's home is a central part of the setting and story, as well. Her isolation inside her home leads to the townspeople (the narrative point of view) having only a partial idea of what she's like. The narrator is on the outside, looking in. Thus, Emily remains mysterious and the surprise ending is achieved. The setting contributes to only glimpses of her personality, and reveals the complete nature of her refusal to change only when she is dead and the house abandoned.