Miss Emily is regarded by her community as a fascinating, old celebrity. She is part of the now extinct "old blood" of the South, of those wealthy families that used to be revered and respected because of the generations of wealth and status that they held. But with the demise of slavery, and the rise of the middle class in America, such reverence for those old families slowly dwindled away, and Miss Emily was the only thing that was left. She was regared by them as an ancient relic, like something in a museum, to be looked upon and wondered at. During her younger years, the townspeople followed her about much like a discredited celebrity, hungry for gossip and opportunities to spread rumors and share in her life. It reminds me of old celebrity have-beens that the paparazzi still follow around simply to report the sordid details of their crumbling lives. The townspeople had the same sense of judgment too; when our favorite celebrity cheats on their spouse, we are upset, we feel angry, and think they should have behaved better. The townspeople feel this way about Emily as she starts hanging around Homer Barron; they are curious and judgmental, and even intervene a bit, as far as they can. And, as the townspeople are the ones narrating this story (it is told, uniquely, from their perspective), we get a good feel for their attitudes and fascination.
Miss Emily doesn't really regard the townspeople at all. They are not worth her consideration, and when they do occasionally step in to try to disrupt her world, she chases them off, maintaining her isolated and skewed perspective of the world that she lives in, where she remains royalty, and the peons of the earthe are below her.
I hope that those thoughts helped; good luck!