First of all, the story is fiction. The category of fiction it falls into is short story. Within the short story, it can be called "regional fiction" or "narrative of community." You might also classify the story within the subgenre of women's fiction.
As for the theme of the story, see the eNotes article linked below. "The White Heron" is a coming of age story, so one of its themes Sylvia's rite of passage from child to woman, from innocence to maturity.