Faith's pink ribbons in Nathaniel Hawthorne's "Young Goodman Brown" essentially represent innocence, and serve as a contrast to Faith's apparent lack of moral soundness.
Pink is traditionally associated with girlhood and innocence; in the cultural setting of the short story, Faith seems to just want to wear the pink ribbons to stand out against the grey and dreariness her fellow Puritans wear. However, as Goodman Brown takes his journey through the woods, he soon realizes that the ribbons are more than just setting Faith apart from the grey crowd, but that they symbolize the difference between being and seeming. Consider this quote from the beginning of the story:
"So they parted; and the young man pursued his way, until, being about to turn the corner by the meeting-house, he looked back, and saw the head of Faith peeping after him, with a melancholy air, in spite of her pink ribbons." (paragraph 6)
Notice the "melancholy air" Faith possesses "in spite of her pink ribbons." This important detail about the pink ribbons helps us understand that though Faith may look childlike, girly, and innocent, she really has lost her moral grounding.