Realism is a literary style employed by writers like Chesnutt who depict in their writing the drama that exists in seemingly uninteresting and unimportant ordinary events.
In the story, Dick Owens is spurred to uncharacteristic action by an exchange with Charity Lomax. The narrator's description of Dick is not particularly exciting; Dick is a privileged, lazy, wealthy young man, which is a character type familiar to many readers. That he is spurred to action by a young woman whose love and admiration he desires is also a familiar story. What keeps these familiar stories from descending into predictable cliche is the realism with which Chesnutt presents the situations and characters involved.
Dick decides to do "something heroic" and "run a negro off to Canada" to gain Charity's devotion. The casual way that he arrives to this action is another example of realism in this short story; though Dick treats the suggestion in a facile manner, the impact of the action on the individuals involved could be potentially quite significant. This potential for drama, presented in the guise of an ordinary conversation, is also typical of literary realism.