The climax of a written work occurs when the tension and action of the plot reach their highest point. This marks a turning point in the story, after which the repercussions of the climax are developed and brought to a conclusion.
The climax of Edgar Allan Poe's "The Black Cat" occurs when the narrator murders his wife with an axe.
The tensions that lead directly to the climax begin when a large, black cat follows the narrator home from a bar one night. The cat bears a striking physical resemblance to Pluto with two exceptions—the cat has one eye and a patch of white fur.
The narrator is kind to the cat at first, but over time, his guilt over having abused and killed Pluto causes him to resent the new cat. The cat's missing eye is a reminder to the narrator of how he blinded Pluto in an intoxicated rage. The cat's white fur patch gradually takes on the ominous appearance of the gallows, further unnerving the narrator.
The story reaches its climax when the narrator and his wife are descending the stairs to their cellar. The cat walks under the narrator's feet, tripping him and sending him into a rage. The narrator tries to kill the cat with an axe, but his wife stops him. His wife's interference further enrages him and he strikes her in the head with the axe, killing her instantly.
This is the highest point of action in the story and the point at which the plot's tension is at its peak. The consequences of the climax include a police investigation, the revelation of the wife's hidden corpse, and the narrator's presumable arrest and sentencing, which in fact sets the stage for the narrator's telling of the story in the first place. As he remarks in the first paragraph, "tomorrow I die, and today I would unburthen my soul."