This is a quote that comes towards the beginning of the story, after Aylmer has his dream about a hand that touches his wife and is the source of the birthmark on his face that he finds so detestable. What is interesting about it is the way in which it reflects Georgiana's love and devotion to her husband. She recognises that he finds something terrible in her birthmark, but rather than ignore it or suffer in silence, she speaks out about it, prompting him to tell her what he is thinking. Just before the quote you have pulled out from the text, the narrator tells us that she speaks quickly so as not to become overwhelmed by her own tears and sadness.
She is a character who is so good and kind and sensitive that the idea of any part of her causing her husband distaste and horror makes her want to cry, but at the same time she confronts him with this idea. She is depicted therefore as a devoted wife who cares more about her husband's love than she does about her own feelings.