The hair suggests not only that Miss Emily has been sleeping with the dead body in the attic bedroom, but that she has been doing so recently. If the hair were of a different color (not grey), we might have assumed that the habit of sleeping with the body was an old one, not a recent one.
Well, the first significance is that the grey hair lets the readers know that Miss Emily has been sleeping with a corpse for years, presumably since Homer's disappearance.
We can move beyond that, as well, and look to what this says about Miss Emily. She was so co-dependent on first her father and then on Homer that she was happy to have him as a corpse if it meant that she could keep him forever. Other posters have covered this well, but I think that an area that you could further explore here is the manservant who left rapidly at the start of the story. He knew that Miss Emily was keeping Homer's body. There is no way that he could not have known. Yet he allowed her to continue her charade. He allowed her to sleep with her dead lover for years, never saying anything to anyone about it. The grey hair on the pillow indicates, at least in the sheltered world of Miss Emily's house, a sense of normalcy that is outside of the realm that most of us consider normal.
I agree with the previous posters. We should not be surprised that Miss Emily is so attached to a corpse, since earlier she refused to let go of her father's. Anyone who is desperate enough to want to have someone stay with her that she will kill him would not--unlike most of us--be daunted by sleeping next to him once he is dead.
The strand of "iron gray hair" is symbolic of Emily's impervious behavior, her iron determination to keep Homer Barron as a lover. In addition, the hair on the pillow indicates that Emily has lain beside the dead man in her "tranquil perversity." That Emily is in love with death has earlier been evidenced when Emily refuses to relinquish the body of her dead father.
If you really look at the references to the passage of time in the story, you can actually put together a time-line to determine for how long Miss Emily may have been sleeping with the dead body of Homer. Consider the description of the color and the length of her hair, and when the narrator reveals that they are pretty sure she shut off the top room of the house and you can surmise that she was sleeping with the corpse for at least 2 years after his death. I don't think it was for the 40+ years he was up there because the pervasive dust of the room had been undisturbed for many years.
I assume that it means that Emily has been sleeping in the same bed with the corpse all these years. It's a long strand of hair and so presumably it's hers. This means that she's really pretty crazy, don't you think? I mean, to sleep in the same bed as a corpse???
So, I think that the hair is supposed to show us just how desperate Emily was to be loved. It led her to kill Homer when he was going to leave and then to sleep next to his corpse all those years.