Noblesse oblige is honorable behavior — considered to be the responsibility of persons of high birth or rank — to members of the lower class.
In Faulkner's short story, the narrator (representing the town's views) is glad that spinsterish Miss Emily now has a love interest in Homer Barron. But that gladness quickly turns to indignation at the very idea of a Northerner presuming to be an equal of Miss Emily, who is a Southern aristocratic lady. The narrator cannot imagine that Miss Emily would stoop so low as "to forget noblesse oblige" and actually become seriously involved with a common Yankee day laborer. In other words, Miss Emily should be courteous and kind to Homer, but she should not become sexually engaged with him.