time with Peyton's body falling through the bridge. It is at this point that Bierce moves us from real external events to real events inside Peyton's mind: "From this state he was awakened--ages later, it seemed to him . . . ." Bierce then takes us through Peyton's physical sensations as he is being hanged. Suffering intensely, Peyton's mind moves next into imaginary thinking (the rope breaks). Peyton's escape does not actually happen. Finally, as he reaches for his wife (imaginary), he feels "a stunning blow upon the back of his neck." With this, Bierce returns to real time as Peyton's falling body reaches the end of the rope, breaking his neck.

Influenced by the writings of Edgar Allan Poe, Ambrose Bierce became intrigued with the significance that the narrator can give to a literary work. It is, indeed, Bierce's artistic and clever use of variations in point of view that often lend realistic shades to his story. There are three variations of narration in "An Occurrence at Owl Creek Bridge": omniscient, third-person limited, and objective. It is the objective point of view which lends the most realistic touches to the story.  For, this type of narration is much like a camera as it reports without comment.  In Section I, for instance, the first four paragraphs are narrated with almost total objectivity. For instance, the second paragraph begins,

Beyond one of the sentinels nobody was in sight, the railroad ran straight away into a forest for a hundred yards, then, curving, was lost to view....The other bank of the stream was open ground...with a stockade of vertical tree trunks, loopholed for riles....

Another aspect of Bierce's story that is realistic are the intentions of the protagonist, Peyton Farquhar.  As a Southerner, he is realistically disappointed that he has been prevented from

taking service with the gallant army that had fought the disastrous campaigns

and he hopes to participate in the glories of war. Contrasted against his dream of glory is the brutally realistic description at the very end of the narrative,

Peyton Farquhar was dead; his body, with a broken neck, swung gently from side to side beneath the timbers of the Owl Creek bridge.

Like so many situations in life, Farquhar's Romantic notions are satirized in the realistic swinging of his dead body.

As a genre of literature, realism can be traced to the mid-1800's, originating in Europe, but quickly reaching the United States.  Realism was particularly well-suited to the time period in which it was born in the United States where nation was teetering on the brink of a Civil War that was forty or more years in the making.  This story by Ambrose Bierce focuses on the hanging of a Confederate spy at a bridge, and the irony of the title is immediately obvious upon reading the opening paragraphs; the fact that the hanging of a human being could be considered nothing more than an occurrence sheds a spotlight on one of the many things that are horrible about warfare. 

The realist writers liked to do just what their name suggests:  write about what was real, what they saw, what they heard, as they saw and heard it.  Realist writers used dialect and local color as tools to create their work, and they also explored the psychological aspects of the human experience.  In this work of fiction, Bierce leads the  reader through a chain-of-consciousness experience that may engender very different reactions from different readers at the end.  Although some critics faulted Bierce for manipulating his readers in a way that was decidedly unrealistic, others have praised this work as being a tightly woven psychological masterpiece. 

In any case, the elements of realism are there in the setting (an Alabama bridge), the descriptions of the characters, particularly Farquhar, the condemned, the psychological ruminations that reel through his mind as he "escapes" and the startling (to some) ending. 

Short answer: The last section seems "real" as it describes the feelings of Peyton Faquhar.

Ambrose Bierce's "An Occurrence at Owl Creek Bridge" is a story told from three separate points of view that serve to cause the reader wonderment about what is real and what is not. These three vantage points are (1) omniscient, in which the narrator is aware of everything about the characters and events; (2) objective, in which the narrator acts much as a camera, reporting without comment; and (3) third-person limited, in which the narrator gives close focus to the thoughts and feelings of one character.

The section that seems the most real to the reader is, ironically, the one that is, in fact, not real. But, because it records the feelings and last thoughts of the main character, Faquhar Peyton, the reader feels drawn into the narrative with Bierce's use of strong sensory images, the use of the third-person limited and, at times, first person narrative. In this third section Farquhar's senses have sharpened and he senses pain as his hands thrust the rope from his neck from his neck.

...his neck ached horribly; his brain was on fire; his heart, which had been fluttering faintly, gave a leap, trying to force itself out of his mouth. His whole body was racked and wrenched with an insupportable anguish!

Further, he experiences the small details of nature with an unusual intensity. And, all the sensations that he feels are so graphic and detailed that the reader is captivated and believing, drawn into the illusion. Nevertheless, the story is real because, although the order of what is described is illusionary, it is only because of the order of what is described; the incidents are real and the sensations of Faquhar are real. For, his experience of having an aching neck and sense of being spun around by the stream and then, finally, his incapability to feel his weary feet certainly could just as well be the feeling of an exhausted man who has escaped as those of a hanged man.