In Sir Arthur Conan Doyle's "The Adventure of the Speckled Band," the exposition introduces Holmes' and Watson's newest mystery to be solved.
A woman arrives early from the train, one Helen Stoner. She lives with her surly step-father who married her mother years before while he was a practicing doctor in India. Her mother is dead, and her sister died several years before just prior to her marriage, whispering something about "the speckled band" with her dying breath.
Though Helen's step-father has not always been so disagreeable, he has become nearly impossible to live with, and he has strange guests living on the estate: a group of gypsies, and a pet cheetah and baboon.
Helen now is also engaged, has been hearing strange noises at night and is frightened for her life. She has come to Holmes', recommended by a mutual acquaintance, for help, but cannot stay long because her step-father would not want her to be there.
These are the important details of the story's exposition: this is where Doyle outlines the mystery Holmes must solve.