Pearl spends most of the narrative as "The elf-child," the ostracized offspring of a forbidden union. Even her play reflects her isolation, where she smites unmercifully "The ugliest weeds in the garden," whom she fancies the children of Puritan elders. Her attitude to her father changes, from caressing his hand early on, to refusing to kiss him in the woods, to finally kissing him on the scaffold. Her transformation occurs precisely at this moment, at the story's end, when Dimmesdale publicly acknowledges her and Hester. It is here she cries for the first time, breaking her spell, and moving her from a girl who would no longer "...battle with the world, but be a woman in it."
This transformation is borne out in her relationship with her peers, from tearing them up as weeds as a child to potentially marrying when she comes of age; when Pearl inherits from Chillingworth, (So Pearl, the demon child...became the richest heiress of the day in the New World) her social standing improves to the point where she could have "mingled her wild blood with the devoutest Puritan of them all."
Pearl, the elf-child, returns to the land of elves and fairies, yet fulfills the prophecy of her being a woman in the world when we surmise that she has borne children and made Hester a grandmother at the very end of the tale.
Up until the moment that Dimmesdale acknowledges Pearl and receives her kiss upon the scaffold, she has been a symbol. She's been the scarlet letter imbued with life, a wild symbol of her parents' sinful union, an elf-child, a symbol of nature like a bird or a flower: but she's never just been a little girl, an innocent child. In this moment, Pearl ceases to be a symbol. The narrator says that when Pearl kissed Dimmesdale's lips,
A spell was broken. The great scene of grief, in which the wild infant bore a part, had developed all her sympathies, and as her tears fell upon her father's cheek, they were the pledge that she would grow up amid human joy and sorrow, nor forever do battle with the world, but be a woman in it. Towards her mother, too, Pearl's errand as a messenger of anguish was all fulfilled.
Thus, Pearl finally becomes a sort of normal human being after this: no longer a symbol of something beyond her but just her. She develops feelings that she's never had before, and no longer seems bound to torture her mother with erratic behavior or childlike obsessions with the scarlet letter. This kiss initiates Pearl into the world. Pearl and Hester return to England after this, and they remain there until Hester becomes an old woman, at which point she returns, alone, to Boston, to live out her remaining days. It was discovered by someone who investigated the lives of mother and daughter many years later that Pearl got married and was happy, "that she would have most joyfully have entertained [her] mother at her fireside." =It seems, then, that Pearl becomes a pleasant and thoughtful young woman without any real trace, it seems, of the mischievousness and wildness associated with her symbolic childhood years.