You probably noticed that there is no rose in the story, though we do find the word "rose" four times. Check out the first two times the word is used:
When the N**** opened the blinds of one window, they could see that the leather was cracked; and when they sat down a faint dust rose sluggishly about their thighs, spinning with slow motes in the single sun-ray. (1.5)
They rose when she entered – a small, fat woman in black, with a thin gold chain descending to her waist and vanishing into her belt, leaning on an ebony cane with a tarnished gold head. (1.6)
These first two times "rose" (as you can see) is used as a verb, which is why we barely notice the subtle echo of the "rose" in the title when we read. We 'e concentrating on the image, first, of the inside of Miss Emily's lonely parlor, and then of Miss Emily herself. In both cases, the word "rose" is working on us, maybe even subconsciously, to contribute to the image.
We have to look at a few more things before we can get at why these passages are significant.
First, let's consider the next two mentions of "rose," which occur at the very end of the story:
A thin, acrid pall as of the tomb seemed to lie everywhere upon this room decked and furnished as for a bridal: upon the valance curtains of faded rose color, upon the rose-shaded lights, upon the dressing table, upon the delicate array of crystal and the man's toilet things backed with tarnished silver, silver so tarnished that the monogram was obscured. (5.4)
Things are starting to make sense: here we're talking about the color "rose." From the curtains to the lampshades, rose is the dominant color of Miss Emily's bridal chamber.
But Faulkner isn't just providing commentary on Miss Emily's interior decorating scheme. We're also getting a strong allusion to the dangers of seeing the world through "rose colored" glasses. Because, when it comes to just about the entire cast of "A Rose For Emily," there's a lot of gazing through pink-tinted specs.
Miss Emily, of course, takes the idea of rose-colored glasses to an extreme: rather than resign herself to the fact that she isn't going to get married, she kills her fiancee and creates a macabre bridal chamber. The townsfolk are also to blame: they view Miss Emily herself through rose-colored glasses. They think of her as a lady—sure, she's a little loony, but she's also above reproach.
And their delusional optimism goes beyond their treatment of Miss Emily. The people of Jefferson also believe that nothing really changed after the Civil War. They still pay homage to the idea of Southern aristocracy—you know, people who money via slavery—was something to be culturally proud of.
But wait—there's more. Lucky for us, William Faulkner shed some light on this title in an interview.
[The title] was an allegorical title; the meaning was, here was a woman who had had a tragedy, an irrevocable tragedy and nothing could be done about it, and I pitied her and this was a salute…to a woman you would hand a rose. (Source)
We think this perspective is very important, not just because it provides a straightforward explanation, but also because it persuades us to indulge in a more compassionate reading. It's easy to judge Miss Emily, and maybe to forget she's a human being who has had a tragic life. (Bonus: for a look at how this explanation exposes the story's irony, check out our discussion of "Writing Style.")