"Exposition" is English teacher language for introduction. Chapter one of "The Canterville Ghost" serves as the exposition (introduction) to the rest of the story, because it gives the reader key details on who the story will be about. It also briefly introduces the setting of the story and the coming conflict that will occur between those characters and that setting.
Chapter one introduces the reader to the Otis family, which is comprised of Mr. and Mrs. Otis, Virginia (their daughter), and the twins. The family has recently bought a really large mansion despite the fact that they have been told that the house is haunted by Sir Simon's ghost. The Otis family ignores the warnings, because they do not believe any of it. They move in the house and immediately begin using their "science" knowledge to clean up supposed blood traces of the ghost.
The blood-stain has been much admired by tourists and others, and cannot be removed."
"That is all nonsense," cried Washington Otis; "Pinkerton's Champion Stain Remover and Paragon Detergent will clean it up in no time," and before the terrified housekeeper could interfere, he had fallen upon his knees, and was rapidly scouring the floor with a small stick of what looked like a black cosmetic. In a few moments no trace of the blood-stain could be seen.