Exposition refers to the background information on characters, setting, and events that will help readers to understand the story.  The exposition in "A White Heron" refers to this kind of information.  It includes the pattern of behavior of Mrs. Tilley's cow and her tendency to run away, as well as information about Mrs. Tilley's granddaughter, Sylvia.  The narrator explains that Mrs. Tilley had chosen Sylvia from her daughter's full house of children in the city, and that people apparently used to say that the little girl was "afraid of folks."  However, since her grandmother brought her to live on the farm in the country, the little girl has thrived and become much happier.  We also learn that Sylvia has a special kinship with the animals in the country and that she loves to be outdoors above anything else.  All of this background information helps us to understand Mrs. Tilley as well as Sylvia, what motivates her, and why she might make the choices that she does as the story progresses.