This is another of Poe's overtly humorous tales, which means that many of its contemporary references went over my head. An over-educated young man becomes a "Doctor of Nosology," thanks to his own sizable proboscis. He enjoys being "lionized" by the literati until he fights a gun-duel with another man, and shoots the man's nose off. Somehow, this loses him all the acclaim he received before, for now his noseless victim is seen as a superior expert on Nosology.
About eight years later, Nathaniel Hawthorne published "The Celestial Railroad," which takes a similar satiric stab at 19th-century intellectual movements, but does so, IMO, with a more skillful sense of the ludicrous.