1. For Gergiana, the birthmark on her cheek with the shape of a hand, represents the idea of morality, this is translated in her constant seek of perfection and also finds the idea of imperfections as the human being nature.
For Aylmer, her birthmark represented her flaws and "liability to sin, sorrow, decay, and death," even though she never made anything sinful.
2. At the end of the story, her birthmark come to symbolize her good spirit and generosity instead of the symbol of death that Aylmer gave it