The house is personified to represent the "Old South" and Miss Emily. The house "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." Now, according to the narrator, industrial progress has "obliterated even the august names of that neighborhood." Here, the house represents the ideals of the "Old South," those of Colonel Sartoris and Miss Emily's father. Even though the house is in decay, it still stands, showing that the attitudes of the "Old South" still remain even in the midst of social and technological progress.
When the narrator says, ". . . Miss Emily's house was left, lifting its stubborn and coquettish decay above the cotton wagons and the gasoline pumps," the house personifies Miss Emily. She is a forced remnant of the "Old South" because of her father's treatment of her and Colonel Sartoris' allowing her not to pay taxes because of her family's name and place in society. Emily, herself, is stubborn and refuses to give in to the community's demand that she pay taxes, just as the house refuses to fall to modernization.
Colonel Sartoris, as a favor to Emily Grierson's father, had upheld the agreement that Miss Emily didn't owe the town any taxes. As government leadership changed, the attitude toward this (or maybe even the knowledge of the agreement altogether was unknown to anyone other than those two men) was disregarded. This is when the men began coming to Miss Emily's house asking her to pay the taxes she owed.
Here is the quote in which the house is personified:
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.
By saying that the house is "lifting its .... decay", Faulkner is imbibing it with human qualities. The reader is left with the impression that the house itself is a stately old Southern madam or gentlemen who lifts his/her head and shoulders and looks down upon those less worth. This story is based on the traditions and social status that dominated the Southern lifestyle. Therefore, the description of the house reinforces the importance of the Grierson's in the tradition of the town.
That story was messed up.