What does pink ribbon symbolize, and how does it relate to faith?
The most common answer to your question is that the pink hair ribbons symboize Faith's innocence and when she loses it so that Brown finds them on the ground it signifies her loss of innocence. But I wonder if the symbolism is as simple as that. Pink hair ribbons would have been frowned upon if allowed at all in the austere of Puritan New England. Most women, married or unmarried would have covered their hair with a cap. So here goes my explanation which may or may not be right.
I believe that one of the theme's of Hawthorne's story is that there is sin in all of us no matter how pious we are on the outside. This is what Brown realizes in his trip (or dream) to visit the devil. Even though these people have claimed salvation, Satan still rules their flesh. Thus the pink ribbons rather than symbolizing purity (they would have been white if that were the case), symbolize the mixture of good and evil (with white for good and the red of Satan for evil) in all of us, including Faith. They, I think, also symbolized the uncertainty of Brown's faith so that when he found them on the ground they represented his loss of faith, and Faith's apparent abandoment of the good half of her for the pure evil of Satan. The fact that the ribbons are in Faith's hair upon his return would signify that she rejected Satan's total controll and signify Brown's still mixed faith.