Pearl is the result of Hester and Dimmesdale's sin and a symbol of their love. Though Pearl is a result of and a reminder of sin, she brings great joy to Hester's life.
Pearl is an active, joyful, unrestrained young girl. Pearl also has an intimate connection with nature. She is not afraid to run, get dirty or speak her mind, and is, at times, uncannily astute (making the connection between Hester and Dimmesdale.) The Puritans associated evil, wrong-doing and witches with the woods (on the edge of which Hester and Pearl live), so Pearl was often seen as a mischievous and ill-behaved child that wasn't being taught or living by Puritan doctrine.
"The child's attire, on the other hand, was distinguished by a fanciful, or, we may rather say, a fantastic ingenuity, which served, indeed, to heighten the airy charm that early began to develop itself in the little girl, but which appeared to have also a deeper meaning." ~ Chapter 4
"Her Pearl!—For so had Hester called her; not as a name expressive of her aspect, which had nothing of the calm, white, unimpassioned lustre that would be indicated by the comparison. But she named the infant “Pearl,” as being of great price,—purchased with all she had,—her mother's only treasure! " ~ Chapter 6 (This entire chapter is about Pearl as is most of Chapter 15.)
"Pearl, whose activity of spirit never flagged, had been at no loss for amusement while her mother talked with the old gatherer of herbs." ~ Chapter 15