First, let's talk about how the story is actually structured. It's divided into three parts. The first part describes the setting and protagonist. A planter from Alabama is about to be hanged from a bridge that spans a rushing creek. He stands on one end of a plank, and a sergeant in the Union army stands on the plank's other end. The planter feels as though time is slowing down, and the sergeant steps aside, off of the plank.
Part II tells us about the protagonist, Peyton Farquhar, in much greater detail. He is ardently devoted to the Southern cause in the Civil War. He is so devoted, in fact, that when a man dressed as a Confederate soldier appeared at his gate one day in the not too distant past, he heard the soldier's declaration that anyone who disrupted the railways would seriously damage the North's war effort with great interest. The punishment for interfering with the bridges and railroads is death. The soldier even described how one might go about setting fire to the Owl Creek Bridge, not too far from Farquhar's plantation. At the end of this section, we learn something Farquhar didn't know: that soldier was really a Federal scout.
Part III describes Farquhar's apparent escape from death when the rope breaks and he falls into the water. He swims amid a hail of gunshots. He walks for many hours through the forest. His thoughts seem to travel "with the rapidity of lightning" during this time. When he finally reaches his home and is about to clasp his wife in his arms, the noose snatches him back and breaks his spine. Farquhar is dead, and his body swings from the Owl Creek Bridge.
The structure, then, makes this story so worthy a piece of literature because of how masterfully each part is executed. Bierce gives readers enough clues to guess at what is happening: Farquhar felt time slow down at the end of Part I; Part II gives us the backstory and explains just how he ended up being hanged in the first place; and Part III contains enough clues for us to understand that what's happening isn't quite right. Farquhar sees details and has experiences that no living person could, and yet, as this section continues (it is the longest of the three parts), we can get a little lost in the story. It's almost as though the exposition introduced in Part II combined with the detail and length of Part III separates us enough from the facts of Part I that we actually begin to believe that Farquhar could have escaped. Thus, it comes as something of a shock—despite the many clues we've had—when his neck snaps. We realize that the entirety of Part III, up until the last paragraph, took place in Farquhar's head, from the moment the sergeant stepped off the plank and he began to fall until the moment the rope stretched taut and his neck snapped. Bierce uses this structure to surprise us but, perhaps, also to humanize a group that is often vilified: Civil War-era Southerners. In a way, we cannot help but care about Farquhar's fate because we begin to empathize with him. Our shock at his death—and, perhaps, at our own sympathy for him—help show how the structure of this text makes it a worthy work of literature.