The Character of pearl was used to Symbolize many things in The Scarlet Letter. One of the main things she was used to symbolize was the joy and sorrow of Hester. Her sins where embodied in the actions of Pearl, Her joy in Pearls and Her sadness in the sadness of pearl. I will speak quickly to each of these three things.
The sins of Hester showed through Pearl in more then one way. The way Pearl acted which was often described, as Impish and Demonic was a direct embodiment of the sins of her mother. Pearl was a strong women who was quick to stand on what she believed, which was a characteristics devolved by Hester because of her sin and giving to Pearl. This can be showed by when Hester removed her A Pearl wouldn't even cross the brook to her mother because she wasn't the same.
The sins of Hester where also cased onto Pearl just because she was born through a bastardly birth and out of wedlock. Through all of these ways Pearl embodied Hester's sins.
All of Hester's joy either came directly from Pearl as in she was just so happy to have Pearl or indirectly as in people where nicer to her because she was raising a child on her own. Hester had a job as a seamstress. People would not have bought Hester goods if it were not for Pearl. The People of that time would not have supported an adulterer for the fear of eternal damnation. Hester was also very happy just to have Pearl as can be showed by that when they where going to take away Pearl Hester Fought with all that she Could to keep her. Hester was a ruined soul that was brought to the light...