) For Georgiana the birthmark represents the idea of death. This symbol can be seen throughout the whole story, through the search of perfection and (understanding/achieving a goal) of (not being perfect) as a part of human being. But her husband understands/explains the birthmark as the hope of/future of death.
2) Aylmer was also promised to/certain that the birthmark represents Georgiana’s moral flaws. He was wrong because she had never done anything sinful. In the end of the story, this mistakenly defined symbol of death on her cheek meetings with her help (by giving money, by sharing, etc.) and good spirit.