Dark Romanticism is a genre that explores the darker, sinful side of man. Think of it as a hybrid between Romanticism and Gothic fiction; it's just that, while Gothic fiction (think Edgar Allan Poe) wanders into horror territory (blood and guts), Dark Romanticism is more interested in psychology, philosophy, and morality. You can see the meaning of the genre right in its name: "Dark" refers to the bleak view of mankind, while "Romanticism" means that it's a sub-genre of the larger Romanticism genre. (In broad terms, Romanticism stressed emotion and aesthetics, made heavy use of symbolism and images, and was a strong rejection of the Age of Enlightenment-driven obsession with science and logic.)
Hawthorne is one of the key players in this genre, and it's easy to see how "The Birthmark" fits the mold. The narrative clearly has its roots in Romanticism if you pay attention to the anti-science sentiments, which many believe Hawthorne expresses. (See "In a Nutshell" for a bit more on Positivism and the scientific world in the 1800s.) And the "dark" part is right on, too – Hawthorne argues that man is inherently flawed, and to make him perfect is impossible. At the same time, he holds up to scrutiny another of man's sins: the ambitious (and problematic) desire to play God.
Because he has a clear point of view, we can see that Hawthorne has some lessons to teach here. In this way, "The Birthmark" is a parable; it uses a very specific situation with very specific characters to make a much broader moral point. Different readers may take away different morals from "The Birthmark," and so we discuss these various perspectives in "What's Up with the Ending?"