Authors in general use symbolism when they are writing about either ideas or psychology. They can't really describe or show what is happening in a character's mind, so they use symbols to convey a sense of their inner thoughts and feelings.
In the case of Pearl, many critics agree that Pearl ultimately symbolizes a happy union between conformity and individual freedom. By the end of The Scarlet Letter, Pearl combines her mother's freedom with her father's respect for social structure. In raising Pearl, Hester sees her own need to control her own strong will. In confessing his sin publicly, Dimmesdale enables Pearl to live a normal life in human society. In other words, he recognizes his need to disregard social opinion for a higher purpose.
Finally, Pearl's behavior might not be entirely symbolic. Hawthorne critics suggest that his own daughter's behavior might have influenced his portrait of Pearl. Apparently, his daughter Una was quite a handful, just like Pearl. I'd also add that Hawthorne wanted to create a very real little girl, not the sentimental, crushingly cute kids that you typically find in 19th century literature.