The single gray hair discovered on a second pillow on the bed where the rotting corpse of Homer Barron lay tells the reader that Miss Emily, above all else was desperately lonely.
It was because of her loneliness that she could not let her dead father go to his grave without a three day wait.
"After her father's death, the ladies reminisce: ‘‘We remembered all the young men her father had driven away.…’’
It was because of her loneliness that she killed Homer Barron rather than allow him to leave her.
"Unlike the majority of the ladies in town, Miss Emily experienced neither the joys of marriage nor the fulfillment of child-bearing."
The important thing about the strand of hair is that it is "iron-gray". On a literal level, this indicates that Emily has been laying her head beside the bones of her dead husband recently. When Homer Barron was last seen alive, Emily was a comparatively young woman; after he disappeared, she herself was not seen for six months, after which she emerged, fat and beginning to gray. The fact that she has kept his body hidden there in her house all these years is made even more horrendous by the insinuation that she has been sleeping by his side during the time that has elapsed since his demise.
On a deeper level, the strand of gray hair signifies age, and the passing of time. Decades have passed since Miss Emily was young; the times have changed, as has the town, and the once proud South has undergone a complete decline. Generations have come and gone, and the only thing that hasn't changed is Miss Emily. She is an anachronism, and the townspeople look upon her with an attitude of curiosity. Emily Grierson is a "fallen monument", an aging symbol of an era that is no longer in existence.
This is meaningful, in the final detail that the strand of hair on the second pillow is iron-gray. That means that Emily was sleeping right next to him all this time. Like a treasure that you never want to give up.