A Rose for Emily" is told in third person limited perspective.
Here is the definition of that point-of-view and its advantages:
Third person limited could be perceived as being told from the viewpoint character. It can be used very objectively, showing what is actually happening without the filter of the protagonist's personality, which can allow the author to reveal information that the protagonist doesn't know or realize. (*as in the case here, where the protagonist does not know until the end what the consequences of his, and the town's, actions have been)
However, some authors use an even narrower and more subjective perspective, as though the viewpoint character were narrating the story; this is dramatically very similar to the first person, allowing in-depth revelation of the protagonist's personality, but uses third-person grammar. Some writers will shift perspective from one viewpoint character to another.