Why does Pearl "burst into a fit of passion"? What calms her, and why?
Pearl, the child of adultery, has seen, since birth, her mother wearing a scarlet "A" on her breast. In chapter 17, when Hester Prynne (her mother) is walking in the forest and meets the minister, Arthur Dimmsdale, Hester suggests, while Pearl is off playing, that Dimmsdale leave this place where he suffers in silence regarding his sin. He says he cannot do it, he hasn't the strength. Hester then tells him he won't go alone, fulfilling his dreams of being with her as man and wife.
Shortly thereafter (in chapter 18), she exclaims with joy, "With this symbol I undo it all, and make it as if it had never been!" She then undid the clasp that fastened the scarlet letter, and, taking it from her bosom, threw it to a distance among the withered leaves." Hester immediately feels the relief of penance done.
In chapter 19, Pearl comes back and stops on the other side of the brook. When her mother calls her to come, she will not. Eventually, She points to her mother's breast with the missing scarlet A. Her mother realizes at this point what the problem is: Pearl does not see something that "is daily before [her] eyes," and is frightened (Hester believes she does not even recognize her without it). Hester points out that the letter lies at her feet, but Pearl won't touch it to bring it to her, as though it's an evil thing, forcing Hester to fetch it and pin it back on before Pearl will come to her. Hester asks if she recognizes her mother now, and Pearl says yes, and comes to her.
Pearl has come to associate her mother with the hated symbol of her sin--so much so that when she reaches her mother, she kisses her and then the letter.