Pearl is the personification of the letter "A" that Hester must wear on her dress as punishment. Hawthorne describes the way Hester dresses Pearl - just as elaborate and fancy as the "A" itself, while Hester remains dressed in drab, colorless clothing. Because of this, Pearl also represents the punishment that Hester must bear. Pearl is the outward symbol of Hester's sin, and because of this, Dimmesdale convinces the town magistrates to allow Hester to keep custody of her. He tells them that Pearl will be a constant reminder of Hester's sin.
This is true, but it is also true that Pearl is a constant reminder of the grace of God. Despite Hester's and Dimmesdale's sin, Hester still received a beautiful gift in the form of Pearl.
Pearl, then, represents the sin, but she also represents the redemption and grace of God.