In Chapter XVIII "A Flood of Sunshine" Hawthorne discusses the change the scarlet letter (and the actions that lead her to have the scarlet letter) has made in her life and how people perceive her.
The tendency of her fate and fortunes had been to set her free. The scarlet letter was her passport into regions where other women dared not tread. Shame, Despair, Solitude! These had been her teachers,—stern and wild ones,—and they had made her strong, but taught her much amiss.
The quote focuses around one of Hawthorne's central theme of sin and knowledge. Because Hester has sinned, she has knowledge of others and can see the sin within them. Unlike Dimmesdale, who still must hide his sin and therefore can never own it, Hester's scarlet letter not only is her atonement for her sin, it also allows her to be bold and experience things that other members of the town cannot.