The best example of symbolism and overcoming adversity comes in Chapter 12, appropriately titled "Another View Of Hester."
At this point in the story, Hester has worn her punishment, the red letter A upon her bosom, for seven years. For seven years she has been seen as the town outcast, the sinner, the scorned. In Chapter 13, however, we are given a new picture of Hester. She is described in this way:
None so ready as she to give of her substance to every demand of poverty...none so self-devoted as Hester, when pestilence stalked through the town...there glimmered the embroidered letter, with comfort in its unearthly ray (147-148).
It is as if by her outcast state Hester finds the courage and duty to reach out to those whom no one else will help. She gives to the poor. She takes care of others who are considered outcasts. The letter which originally was meant to bring only shame changes in meaning:
many people refused to interpret the scarlet A by its original signification. They said that it meant Able; so strong was Hester Prynne, with a woman's strength.
This also foreshadows Hester's continuing journey toward courage and healing. By the end of the story, she dies with a legacy, not of sin and shame, but of a woman who overcomes.
My favorite symbol of overcoming adversity in The Scarlet Letter is the rosebush in the opening chapter. The prison ultimately symbolizes social convention and codes. The rosebush symbolizes human nature, most specifically, the good in human nature.
Hawthorne shows that the Puritans try to control human nature with strict laws and codes. What he also shows is that the Puritans' attempts to control human nature either make it more rebellious or else result in the judgment of certain individuals who aren't necessarily "criminals."
An example of how the Puritan rules make human nature worse is when he refers to the prison house as a "black flower" of civilization. Hawthorne suggests that maybe crime results as a result of overly strict rules, not from the "sinfulness" of human nature the Puritans believe in.
An example of how the Puritan rules result in the wrongful judgment of individual rebels or dissidents is Hester Prynne's imprisonment. The Puritans call her a "criminal" or a "sinner," but Hawthorne shows that what previous generations called a criminal, our present society calls a "feminist."
The rosebush represents the hope that the good in human nature will survive overly strict social codes and find some kind of happiness in the world. Hawthorne later associates the rosebush with Pearl, showing that Hester's and Dimmesdale's affair--their "criminal" act of "sin"--had a happy ending in Pearl's escape from Puritan society and a happy life in Europe at the end of the novel.