Aylmer absolutely detests the little red birthmark shaped like a hand on his wife's left cheek. To him, it is a blemish on an otherwise perfect face. As a famed scientist, he has traveled all over the world, using his vast knowledge to solve problems, and he's absolutely determined that this particular problem—his wife's unsightly birthmark—will also be solved. To this end, Aylmer has invented a special potion which he believes will remove Georgiana's birthmark once and for all.
Aylmer's (over) reaction to his wife's slight physical flaw tells us a lot about his character. This is a man who simply cannot and will not accept his wife for what she is, warts and all. (Or in this case, birthmarks and all.) Aylmer comes across as a bit of a control freak, someone who always has to have his own way. His wife is no more to him than a guinea pig for his latest experiment, someone to be controlled and exploited for the advancement of scientific knowledge. He's also something of a perfectionist; everything in his life must be just right. That's why he finds the very sight of his wife's birthmark so incredibly offensive.
Despite being a man of science, Aylmer largely inhabits a world of his own imagination, and in this ideal world, everything is just as it should be, including Georgiana. He becomes so obsessed with making his crazed fantasy world a reality that he's prepared to risk the life of Georgiana, the woman he's supposed to love.