Aylmer is a late 18th-century scientist who is totally and completely committed to his work. His entire life has been about figuring out the way that nature works, to the detriment of his personal and social life. However, just recently, he has put down his test tubes long enough to marry a beautiful woman, Georgiana.
Now, Georgiana is distinctive in that she has a small red birthmark on her cheek in the shape of a tiny hand. Most men who pursued her found the birthmark attractive; some catty women said that it messed up an otherwise perfect face. Georgiana has always liked it, until Aylmer brings up the topic one day soon after their marriage. He doesn't like the birthmark; he thinks Georgiana would be perfect if it were removed.
Georgiana falls completely to pieces. Because Aylmer thinks the birthmark is ugly, she now thinks herself ugly, and both partners become increasingly unhappy in their marriage. In Aylmer's mind, the birthmark becomes the symbol of human imperfection. Some time later, Aylmer tells his wife of a dream he had, in which he tried to surgically remove the birthmark. The deeper he cut, he explains, the deeper the birthmark went, until it was a part of Georgiana's very heart. In the dream, he wanted to keep cutting through her heart to get it out.
Georgiana is so upset by this dream that she tells Aylmer to figure out a way to get rid of the birthmark. Aylmer has already been working on such a plan. He takes Georgiana into his laboratory, where he has set up a special room for her to hang out while he devises an elixir with which to remove the birthmark. In the laboratory we meet Aminadab, Aylmer's assistant, who is stocky and earthly in contrast to the spiritual and lofty Aylmer.
When the elixir is finally ready, Aylmer brings it to his wife, who drinks it and falls asleep. Sure enough, the birthmark fades almost entirely from her face. Aminadab laughs at the outcome rather cryptically. Sadly, Georgiana wakes up, she tells Aylmer that she is dying. Then, as we might expect, she dies. Aminadab laughs again, which we have to say is rather untactful. The narrator then takes over for the conclusion to tell us that Georgiana couldn't live as a perfect being, since human beings are necessarily imperfect. Also, he says, Aylmer is kind of an idiot for throwing away a good thing (a good thing being the beautiful woman who is now perfect, but also dead).