Emily is symbolic of many things, including the "Old South," as the editor above mentioned.
Emily also represents the resistance the "Old South" had to changing from an agricultural society to an industrialized one. After the Civil War, it was inevitable that the South would have to become industrialized; however, there was still much resistance to this from many Southerners. This is one of the reasons why the change took a while to become reality. Emily also resisted change and the new ways that were permeating her town. She chose to live in a "bubble" and ignore what was going on around her.
Emily also represents the decline of the "great Southern family" that had so much influence on politics, government, and social life.
Another thing the rose might symbolize is the love that Miss Emily never ended up receiving. She longed for it, but it never came to fruition.
Emily is a symbol of the Old South and its way of life which was steeped in tradition. Even though she comes from an old, respected family, her father leaves her so poor she cannot pay her taxes. Out or respect for tradition, she is excused from paying taxes. This tradition continues in the story and is one of the main reasons no one questions her about the smell around her house. As for the rose, there are many explanations for the rose, most having to with the qualities and uses of roses. For instance, a rose is a beautiful flower but it has nasty thorns. Emily shows some pretty nasty thorns in her response to Homer. William Faulkner, the author, said the rose in the title meant the story was a tribute to Emily. Thus, the rose's symbolism can be left up to the reader.