Why Dimmesdale keeping her identity secret.

 A man and a woman, who are still essentially the old Adam and Eve, deceive themselves into thinking that they can escape the consequences of their sin of adultery. The woman serves a prison term and has to wear on the bosom of her dress the letter "A" which is the sign of her shame. The man, who was the occasion of that shame, lives a life full of torture because of his inability to confess his guilt and because of the remorse which gnaws upon his conscience. Meeting in the forest, they plot an escape from the world of law and religion. For a moment, the hope of liberation seems to transfigure not only them but the dark forest where they have met. When Hester flings aside the scarlet letter and loosens her hair, the forest glows to life because of Nature's sympathy with the lovers and its approval of their bliss. Yet Hawthorne cannot permit these lovers the happiness that they seek. He is not as harsh as his Puritan ancestors, but he condemns Hester's plan of escape.

For all his disagreement with Puritanism and its persecuting zeal, he does not swerve completely to the side of romanticism which means unlimited freedom for the individual. The sinful priest purifies himself by public confession and becomes worthy of the only way that remains for him to salvation, namely death. Even Hester  must finally accept loneliness and self-restraint instead of the love and freedom she had dreamed. Passion has opened up for her no new possibilities, only closed off older ones. Thus in The Scarlet Letter, passion justifies nothing, while its denial redeems all."

When it is known that she is pregnant, she is sent to the scaffold for committing adultery. She later gives birth to her daughter, Pearl, and is forced to wear a scarlet letter “A”  on her bosom, which stands for adultery.

Seven years have passed since Pearl’s birth. Hester has become more active in society. She brings food to the doors of the poor, she nurses the sick, and she is a source of aid in times of trouble. She is still frequently made an object of scorn, but more people are beginning to interpret the “A” on her chest as meaning “Able” rather than “Adulterer.” Hester herself has also changed. She is no longer a tender and passionate woman; rather, burned by the “red-hot brand” of the letter, she has become “a bare and harsh outline” of her former self. She has become more speculative, thinking about how something is “amiss” in Pearl, about what it means to be a woman in her society, and about the harm she may be causing Dimmesdale by keeping Chillingworth’s identity secret.