The sin, punishment, and redemption are most clearly illuminated by Hester Prynne. First, she commits the sin of adultery. Her husband never arrived from Europe, and though he is believed to be dead (since he's been missing for two years), his death has not and cannot be confirmed. Therefore, since he could still be alive, Hester has technically committed adultery, and her sinfulness is betrayed by her pregnancy.
Hester is punished for her sin with a little jail time, a shaming on the scaffold, and the rule that she wear the scarlet A on her chest at all times. This letter seems to cast a spell around her, separating her from everyone else. Even in crowds, a little magic circle seems to be drawn about her, and people keep out of a certain radius. This punishment affects her daughter as well -- other children will not play with her. Sometimes, they throw mud at Hester and Pearl, and sometimes Hester walks in to Sunday services to find that she is the subject of the sermon. In addition to her scarlet A, Hester essentially endures the life of an outcast; there is, once, even talk of taking her daughter away from her. Even the poor folk to whom she gives her extra money and food spit insults at her when they see her.
Hawthorne's suggestion, which is made through this illustrative logical circle of sin -- self -- others, is that redemption for one's sin originates in knowledge of and understanding of one's self to such a depth that its natural extension is to know and understand humanity. Hawthorne implies that such knowledge and understanding leads to an embrace of others. This is sharply contrasted to the Puritan community's practice of expelling humanity, such as Hester, when humanity in the form of the individual is caught in sin. Further, Hawthorne suggests that the embrace of humanity via the individual other leads from redemption to the renewal of purity, a purity that is opposite of the Puritan community's hollow, meaningless purity -- which is the purity of expulsion.
Officially, Hester can never really be redeemed by the laws of her community; however, she seems to redeem herself in the eyes of her community if not its laws. The more Hester ministers to the sick and the grieved, people begin to whisper that her "A" now stands for angel instead of adulterer. They begin to call her "our Hester," and to take a sort of pride in her good works. She has clearly atoned for her sin.
In the end The scarlet letter ceased to be a stigma which attracted the world's scorn and bitterness, and became a type of something to be sorrowed over, and looked upon with awe, yet with reverence, too."
