Why does Hester choose to stay in the town?
Hester Prynne did not leave the Puritan village, because "She could no longer borrow from the future, to help her through the present grief." That means she could not trust in the future, not be sure to get better.
Furthermore, "there is a fatality, a feeling so irresistible and inevitable that it has the force of doom, which almost invariably compels human beings to linger around and haunt, ghost-like, the spot where some great and marked event has given the color to their lifetime; and still the more irresistibly, the darker the tinge that saddens it. Her sin, her ignominy, were the roots which she had struck into the soil. It was as if a new birth, with stronger assimilations than the first, had converted the forest-land, still so uncongenial to every other pilgrim and wanderer, into Hester Prynne's wild and dreary, but life-long home." That means that she has a special feeling that she should stay here in her "new" home, no matter what has happened.
Another reason might be "All other scenes of earth--even that village of rural England, where happy infancy and stainless maidenhood seemed yet to be in her mother's keeping, like garments put off long ago--were foreign to her, in comparison. The chain that bound her here was of iron links, and galling to her inmost soul, but never could be broken." She says that the chains or the connections to the village where she was born and has lived for her whole childhood are broken, that she does not feel to have a real relation to her village in her home county.
Finally "she said to herself, had been the scene of her guilt, and here should be the scene of her earthly punishment; and so, perchance, the torture of her daily shame would at length purge her soul, and work out another purity than that which she had lost; more saint-like, because the result of martyrdom." That means that she feels guilty and wants to get her punishment at the place where she did her crime. And she knows that she will experience a lot of mortification.
How does the community treat her?
The community treats Hester very bad. She had to live in a very poor shelter away from other homes. She had no single friend. Later, the people of Boston tried to take her child away from her. She was treated as a victim with mortification,animosity and contempt. Having a child without marriage or from another man than her husband was a very bad crime for this time, especially for Puritans. Hester was excluded from her people.
