As the title of the short story suggests, "The Wonderful Story of Henry Sugar" tells the story of Henry Sugar, a wealthy man with a penchant for gambling. One day, Henry discovers a doctor's report which describes a strange patient from India who was able to see despite the fact that his eyes were shown completely shut by doctors. To that end, the man uses his strange abilities to conduct a very interesting and incredibly lucrative act for the circus.
After reading for a short amount of time, Henry discovers that the method by which the doctors "removed" the man's sight. Henry conducts the procedure, and eventually gives himself the power to see despite his sewn-shut eyes.
With the help of his powers, Henry undergoes a series of charades designed to make him a tremendous amount of money. This is something which he succeeds in doing, but not without a significant cost.