Homer Barron comes into town from the North in charge of the men paving the sidewalks. The narrator calls him
a Yankee - a big, dark, ready man, with a big voice and eyes lighter than his face... whenever you heard a lot of laughing anywhere about the square, Homer Barron would be in the center of the group.
Miss Emily is undoubtedly attracted to his confidence and personality - and perhaps the fact that he is different. He is different, certainly than she is, but different from the rest of the town. In fact, he's looked at as taboo as a result of that - and perhaps Miss Emily likes the idea of doing something wrong after years of living with a very stern father. It turns out Homer Barron is also a homosexual. It is never said whether Miss Emily knows this or not - however we assume he eventually does not return affection for her which is one reason why she might have killed him.