Realism in literature is an attempt to present a story without the use of romanticism or idealization. Basically, the story was to be told as it would have really taken place, or without objectivity. In Ambrose Bierce's short story, "An Occurrence at Owl Creek Bridge," the narrator seems to be telling the story factually until the reader reaches the ending.
In "An Occurrence at Owl Creek Bridge," the reader does not realize that the narrator's perception of time has become very distorted. Part of the reason for the this is the narrator's point of view, which begins as objective, but moves moves to third-person limited; also, the use of stream-of-consciousness is very effective in keeping the reader uninformed as to the reality of what is happening to Peyton Farquhar.
Because the reader believes that the events of the story are being relayed reliably and factually, the reader excuses illogical or improbable occurrences, such as Farquhar's avoiding not only hanging, but also drowning and being under direct gunfire from a trained marksman and an attack by cannon. Bierce utilizes literary techniques so cleverly that reader is truly surprised to find that the events of the story took place during Farquhar's actual hanging.