Miss Emily is allegorical in this story because she represents the "old" South. She is the great, old "Grand Dame" of the South, the "Southern Belle," if you will. She also represents the inability to change and what happens when one is not willing to change with the times. Her own physical deterioration and the deterioration of her home mirror the deterioration of the old ways of the South (an agricultural-based society).
The story is allegorical, also, in that it is representative of the old, outdated, at times comical, ways and traditions of the "old" South. Faulkner was very familiar with these traditions and ways; eNotes states that:
Originally, the town was governed by men of the old South like Colonel Sartoris and Judge Stevens. Men like this operated under a code of chivalry that was extremely protective of white women. Thus, Colonel Sartoris is unable to allow the town to tax a poor spinster, and Judge Stevens is unable to confront Emily about the smell coming from her house. As each generation passes the torch, however, the newer generations are further and further away from the antiquated social mores of their forebears.
An allegory is a story in which the characters and the events of the story are symbolic, all designed to express an overall symbolic message. In this story, the allegory is a commentary on the relationship between the North and the South after the Civil War. The town, Emily, and the relationship between the two are representative of the South. Emily is "old family", and the town treats her as such. The respect the family and give it a wide berth, not even going into the house when a foul smell emanates from it into the rest of the town. Emily, in her isolationist ways, shows the unwillingness of the South to change, despite being "invaded" by the influence from the North.
The "the next generation, with its more modem ideas, became mayors and aldermen" tried to change the ways of Emily, but ultimately they failed. When they demanded taxes, she refused to pay, and she won. This is symbolic of the South's determination to retain its character and its culture.
Besides the "next generation", Homer Barron - a Northern carpetbagger - represents the North after the Civil War. Homer, like the North, came in and had an impact on Emily. He tried to leave, as many of the carpetbaggers did after Reconstruction. Emily was having none of that, and killed him. Faulkner is delivering a strong message for the power of the South, despite what it suffered during Reconstruction.