There are several themes in the story death, the decline of the Old South, and community vs. isolation. The story begins with Emily's funeral; previously Emily's father, Colonel Sartoris, and Homer Barron also died. It is Emily's inability to accept the death of her father and others that are important to investigate regarding the theme of death in "A Rose for Emily". The theme of the decline of the Old South is mirrored in the description of Emily as she ages and her hair turns more and more gray; her house becomes dilapidated and dust covers the furniture. The dust, decay, and mold relate how the values and institutions of the Old South have lost thier vigor. The theme of community vs. isolation is developed as Emily is isolated from interested young men because her father thinks a Grierson is too good for the men of Jefferson. Although, Emily is isolated from the community, the people of the town are almost obsessed with her and hold her in high regard as a idol of the Old South.
You'll find detailed discussion of the themes of this story in that section of the enotes study guide on the story: http://www.enotes.com/rose-emily/7077
As you read through the section of the study guide titled "Summary and Analysis," you'll also find thematic discussions there.