Miss Emily's house is an important symbol in this story. (In general, old family homes are often significant symbols in Gothic literature.) For most of the story, we, like the townspeople, only see Miss Emily's house from the outside looking in. Let's look at the some of the descriptions we get of the house:
It was a big, squarish frame house that had once been white, decorated with cupolas and spires and scrolled balconies in the heavily lightsome style of the seventies, set on what had once been our most select street. But garages and cotton gins had encroached and obliterated even the august names of that neighborhood; only Miss Emily's house was left, lifting its stubborn and coquettish decay above the cotton wagons and the gasoline pumps – an eyesore among eyesores. (1.2)
The fact that the house was built in the 1870s tells us that Miss Emily's father must have been doing pretty well for himself after the Civil War. The narrator's description of it as an "eyesore among eyesores" is a double or even triple judgment. The narrator doesn't seem to approve of the urban sprawl. We also speculate that the house is an emblem of money probably earned in large part through the labors of slaves, or emancipated slaves. The final part of this judgment has to do with the fact that the house was allowed to decay and disintegrate.
For an idea of the kind of house Miss Emily lived in, take a look at artist Theora Hamblett's house in Mississippi, built, like Emily's, in the 1870. Now picture the lawn overgrown, maybe a broken window or two, the paint worn and chipping and you have a the creepy house that Emily lived in, and which the children of the "newer generation" probably ran past in a fright.
The house, as is often the case in scary stories, is also a symbol of the opposite of what it's supposed to be. Like most humans, Emily wanted a house she could love someone in, and a house where she could be free. She thought she might have this with Homer Barron, but something went terribly wrong. This something turned her house into a virtual prison – she had nowhere else to go but home, and this home, with the corpse of Homer Barron rotting in an upstairs room, this home could never be shared with others. The house is a huge symbol of Miss Emily's isolation.