Who is Pearl?

Pearl is the Hester Prynne and Arthur Dimmesdale's illegitimate daughter. Although Hester was married (albeit estranged from her husband), she and the reverend engaged in sexual conduct, resulting in a pregnancy. Unwilling to expose him, Hester bears the burden of her sin publicly, letting Dimmesdale to suffer in shadow.
Hester is condemned to wear the letter "A" on her chest as a reminder and a warning against adultery, but Pearl stands out as a more potent symbol of their union. While the embroidery of the letter generates negative feedback at first, as was its purpose, the scarlet letter takes on new meanings with time. Instead of constantly speaking of her sins, the symbol becomes regarded as meaning "Able," due to Hester's strength. Pearl, on the other hand, refuses to let her mother forget the act or attribute positive qualities for her illicit love.
In Chapter 15: Hester and Pearl, the young girl makes a connection between her mother's letter "A" and the reverend's perpetual hand placement over his heart. When asked if she knows why she wears the letter, Pearl replies:
"Truly do I! ... It is for the same reason that the minister keeps his hand over his heart!"
Pearl continues to implore her mother for answers, but receives no response.
Later, in Chapter 19: The Child at the Brookside, Hester and Arthur stand on one side of a brook planning an escape to be together again. Hester casts off the letter, hoping to be free, but Pearl refuses to come to her until her mother pins it to her chest again. Unlike the piece of fabric, Pearl cannot be simply removed or purged. Instead, she takes on the characteristics of her mother and father, making their affair harder to hide.

The theme of the novel is based on a famous incident recorded in John, Chapter 8, of the New Testament.
And the scribes and Pharisees brought unto him a woman taken in adultery; and when they had set her in the midst, They say unto him, Master, this woman was taken in adultery, in the very act. Now Moses in the law commanded us, that such should be stoned: but what sayest thou? This they said, tempting him, that they might have to accuse him…. So when they continued asking him, he lifted up himself, and said unto them, He that is without sin among you, let him first cast a stone at her. And again he stooped down, and wrote on the ground. And they which heard it, being convicted by their own conscience, went out one by one, beginning at the eldest, even unto the last: and Jesus was left alone, and the woman standing in the midst. When Jesus had lifted up himself, and saw none but the woman, he said unto her, Woman, where are those thine accusers? hath no man condemned thee? She said, No man, Lord. And Jesus said unto her, Neither do I condemn thee: go, and sin no more.
Pearl not only represents the sin of adultery, but Hawthorne calls her “a living hieroglyphic.” She is not only proof of the sin, but as she grows older the features of her father will become more and more apparent in her own. In other words, Dimmesdale’s guilt will become obvious to everyone sooner or later, because Pearl will look more and more like her father.
Hester names her child Pearl because she is a treasure for which she has had to pay a great price. Here again, there is a direct allusion to the New Testament. In this case it is to Matthew 13:45-6.
Again, the kingdom of heaven is like unto a merchant man….Who, when he had found one pearl of great price, went and sold all that he had, and bought it.
Pearl is already a complex character while still very young. She is exceptionally beautiful, but at the same time she is described as having a mischievous and impish nature. Her mother loves her and refuses to part with her, but at the same time she is a little bit afraid of her, as are all the other children for that matter. Pearl is a continual source of worry for both her parents. Hawthorne apparently intended to convey that idea that this little girl has a conflicted nature because she was born out of a sinful liaison and is growing up without a father. In his novel The House of the Seven Gables, Hawthorne’s theme was based on Exodus 34:6-7 in the Old Testament:
...The Lord, the Lord God, merciful and gracious, long-suffering, and abundant in goodness and truth, keeping mercy for thousands, forgiving iniquity and transgression and sin, and that will by no means clear the guilty, visiting the iniquity of the fathers upon the children, and upon the children's children, unto the third and to the fourth generation.