This story is based on the short story (and later a novel) "Flowers for Algernon", in which an experiment temporarily turns a mentally retarded man into a genius. The most direct reference to the book is the white mouse that repeatedly beats Homer in a game, just like Algernon (a white mouse as well) beats Charly in the original story.
This episode was written by current show runner Al Jean and directed by supervising director Mike B. Anderson. Jean based the episode's plot on Flowers for Algernon, a novel which he had read in the 8th grade, which was made into the movie Charly (1968); the source of this episode's title.
We learn that Homer's IQ is 55. According to the DSM-IV guidelines this puts him on the bottom end of mild mental retardation. To be considered moderately retarded, one must have an IQ of less than 50.
During the couch gag Philip J Fry is put in place of Bart then swapped. Fry is from Simpsons creator Matt Groening's other show Futurama.
The episode won an Emmy Award for Outstanding Animated Program.