The references to the Civil War help establish the setting and culture of the community, and Emily’s importance to the town.
The first reference to the Civil War tells you instantly that the story takes place in the South.
And now Miss Emily had gone to join the representatives of those august names where they lay in the cedar-bemused cemetery among the ranked and anonymous graves of Union and Confederate soldiers who fell at the battle of Jefferson.
Clearly the war is important to these people, as it was for many Southerners. Long after the war the role your family played in it was important to your status. This is why Emily’s father is referred to as Colonel Sartoris. He retained his title, and is called Colonel rather than mayor.
Emily’s sense of entitlement comes partly from having a war hero as a father, and partly from having a mayor for a father. It affects her own actions, and how others treat her,
The overtone of war, death, and decay hovers over the entire story. There is also a stubbornness associated with the Southerners after the war, many of whom did not want to think of themselves as losers. This pervades the town, and Miss Emily. Southern gentility aside, there is pride in being a Southerner.