As Peyton Farquhar prepares to die in "An Occurrence at Owl Creek Bridge," he hears "a sharp, distinct, metallic percussion like the stroke of a blacksmith's hammer upon the anvil." These sounds become less frequent even as they increase "in strength and sharpness." This effect, the author tells the reader, is produced by "the ticking of his watch," though it is not clear that Peyton himself is aware of this.
Although this story, like any work of literature, can be interpreted in various ways, the most common interpretation is this: the entire story takes place in a few moments, and Peyton Farquhar's escape occurs entirely in his mind as he falls through the bridge, just before his neck is broken. In these last moments before death, his perception of time slows down, as his dreamlike state becomes extraordinarily vivid. His attention has been caught by the ticking of his watch, which is why this heightened perception makes the ticking sound louder, even as the effect of time slowing down makes the intervals between sounds seem longer. The length of time between sounds also intensifies their volume, as far as he is concerned.
There is no indication that anyone else hears Peyton's watch ticking. His perception that the sounds are growing louder is caused by his heightened and distorted perceptions in the moments immediately before his death.