Why is the story "A Rose for Emily" divided into parts?
Faulkner doesn't present things chronologically. Instead, he seems to organize things topically, and the breaks coincide with those topics. The first topic is her death, the second her taxes, the third the smell, the fourth her father's death and Homer Barron, and lastly, the horrific discovery. It is an interesting way to tell a story-topically-but it helps the reader piece things together just the same, and allows Faulkner to present all pertinent information in the order that best helps us to understand Emily's character by the end.
The breaks allow for this topical arrangment, and for the reader to be suspicious as they process things in-between each subject change. Faulkner uses the subject changes and breaks to switch to the next relevant topic, and to give clues along the way to what happens in the end; that way, it makes a bit more sense to us. He tells it more like a brain would think it; he mentions one thing, which reminds him of another thing because it directly applies, and by the time we get to the end, we have a full picture. It also provides great entertainment as we go through and read it a second time, because we pick up on clues that weren't obvious the first time.