In chapter 13 "Another View of Hester" from The Scarlet Letter we see how the town's view of Hester and her ignominious letter has changed over the past seven years.
Because she has sinned, she has the ability to not only see it in her fellow Puritans, but she is also able to support and comfort them. The letter still stands out to the town, but it has begun to serve as a lighthouse for those searching for comfort and a place to find solace.
There glimmered the embroidered letter, with comfort in its unearthly ray. Elsewhere the token of sin, it was the taper of the sick-chamber. It had even thrown its gleam, in the sufferer's hard extremity, across the verge of time. It had shown him where to set his foot, while the light of earth was fast becoming dim, and ere the light of futurity could reach him.
Unlike those who were so quick to turn their backs on her, she was willing to offer a shoulder to cry on. By calling her a "self-ordained Sister of Mercy," Hawthorne is showing the reader how Hester has taken it upon herself to tend to the sick, help the poor, and listen to the brokenhearted.
In such emergencies, Hester's nature showed itself warm and rich; a well-spring of human tenderness, unfailing to every real demand, and inexhaustible by the largest. Her breast, with its badge of shame, was but the softer pillow for the head that needed one. She was self-ordained a Sister of Mercy; or, we may rather say, the world's heavy hand had so ordained her, when neither the world nor she looked forward to this result.
Unlike the harsh gossips who judged and criticized her in Chapter 2, she has the power to sympathize and listen to her fellow man. Surprised by this change, the town begins to stop regarding her letter as a symbol of her "adultery" and more a symbol that she is "able."
The letter was the symbol of her calling. Such helpfulness was found in her,—so much power to do, and power to sympathise,—that 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.