The point of view is that of the town itself, told from an unnamed narrator’s perspective but sharing the town’s feelings.
The point of view of the story is first person, but not the typical first person. There is not one named narrator whose mind we follow. Instead, it is “our town.” It is almost as if the town itself is telling the story, or one person is sharing multiple perspectives gleamed from rumors. Small towns tend to have a collective consciousness. It is this consciousness that narrates the story.
As the daughter of the town patron, Miss Emily kind of belongs to the town. It is a bit like how we view celebrities today. She is the object of scrutiny and curiosity. Her father considered the town to belong to him, so she did as well. As a result, she belonged to the town.
An example of this is the description of how Miss Emily stopped coming out of the house.
That was two years after her father's death and a short time after her sweetheart--the one we believed would marry her --had deserted her. After her father's death she went out very little; after her sweetheart went away, people hardly saw her at all.
The use of “we believed” and “people hardly saw her at all” demonstrates this collective consciousness. The town puts its information together, and the town is the narrator.
The result of this narrative style is that it creates suspense. We do not quite know what is going to happen, because we never really get the entire picture. Instead, it's like listening to a juicy rumor- you know it is going to end in an interesting way, but you are not sure how.