How does Hester use her punishment to improve herself in The Scarlet Letter?

Ironically, it
is the non-Puritan Hester, and not the Puritan minister Dimmesdale, who makes retribution for
her sin of adultery. Hester, for whom the scarlet A is a mark of
humiliation, willingly accepts this humiliation in lieu of drawing suspicion upon her partner in
sin. Thus, Hester's salvation lies in "being true" as Hawthorne exhorts in one of the
final chapters.

• When she is interviewed at the Governor's Hall,
  Hester defiantly accepts her punishment as she dressesboldly in crimson. She pleads to be
  allowed to keep Pearl:

God gave me the
child...in requital of all thing else....She is my happiness!--she is my torture, note the
less!....Peal punishes me, too!  See ye not, she is the scarlet letter, only capable of being
loved,a nd so endowed with a millionfold the power of retribution for my sin?

As a reminder of her sin, Pearl directs Hester's future
behavior.

• The scarlet letter becomes "...her passport into
  regions where other women dared not tread." She it is who cares for the ailing and aged;
  she it is who assists with the funeral arrangements for the dead, she it is who tends the
  wretched. After she spends considerable time nursing many in the community, the perception of
  Hester's A changes to become a symbol of her abilities: it is read as
  "Able" and "Angel" by members of the community and becomes "the symbol
  of her calling." To the "afflicted," the effect of Hester's scarlet letter for
  which she has done penance and performed many a good dead is that it has become a badge of her
  calling:

...the scarlet letter had the effect
of the cross on a nun's bosom. It imparted to the wearer a kind of sacredness, which enabled her
to walk securely amid all peril.

• In Chapter
  XII, after tending the sick late at night, Hester and Pearl pass the minister, who stands upon
  the scaffold. With Pearl, Hester joins the Reverend Dimmesdale upon the scaffold, feeling there
  is a responsibility towards him that she must fulfill.
• Another improvement
  to Hester as a result of wearing the scarlet letter is that Hester abandons passion for thought.
  In a sense, she becomes a modern woman, one who thinks for her self and considers existential
  problems. As such, too, she is able to reason with Dimmesdale in the forest in Chapter XVII and
  encourage him, providing him counsel about their future and about . For Dimmesdale, Hester
  becomes his "better angel!"
• Certainly,becomes a much stronger
  person as a result of her sin, its humiliation, and her repentance. And, unlike , "false to
  God and man," Hester has remained true.