In chapter 13 of The Scarlet Letter, how has the "A" freed Hester?
By this stage of the novel, Hester has gained a measure of acceptance by the Puritan community. She has taken her punishment, makes no trouble among the people - indeed, on the contrary, she does a great deal to help them. She has come to be known as a charitable type who people can turn to in times of trouble. The A on her breast is now taken by some not to represent her sin but rather to stand for 'Able'.
However, although she outwardly conforms to the strict conventions of the community, inside she retains all her independence of spirit. Having been literally marked for adultery, she essentially remains at the edge of society - and this position gives her a clearer view on that society and its failings. She sees how limited women really are, restricted not only by men but also their own narrow image of themselves . She realises that new foundations for society have to be built to improve things all round. This is an advanced sociological view for the time, but Hester has managed to gain it through the unique vantage point that the scarlet letter puts her in. We might say that the scarlet letter has made her 'able' to see things more clearly, that it has given her freedom of thought.