In what two ways does the title relate to the story?

The title of the story "The Black Cat," though simple, is rich in meaning when considered in light of the story's literal and figurative interpretations. On a literal plane, the story features not one, but two black cats. The first cat, Pluto, has been the family cat for years and is devoted to the narrator, and the narrator states that he had been devoted to it in earlier years as well. However, as the narrator descends further into alcoholism, he becomes "peevish" at the cat, and one night, in a drunken fury, cuts out one of its eyes with a pen knife. After that, the cat avoids him, and the man, giving way to "perverseness," hangs the cat. As if in retribution, the man's house burns to the ground that night. 

At his new home, the man ends up adopting a stray cat, also a black cat, that is similar to Pluto, even in having one bad eye. The man begins to dislike, then loathe, the cat, but it sticks close to him. Then an outline appears on the cat's chest of a gallows, reminding him of his horrible deed to Pluto. The narrator then tries to kill the cat, kills his wife instead, and the cat ends up revealing the narrator's crime to the police. The use of the singular for "cat" in the title implies that the two cats are one, that the second is merely a reincarnation of the first. That is implied early in the story when the narrator relates his wife's opinion that all black cats are witches in disguise. 

On the figurative level, one can consider whether the "black cat" of the title refers not to the felines at all but rather to the narrator himself. If, as suggested by the narrator, black cats are witches, that presents a black cat as the personification of evil. Black is also a color that is symbolically associated with evil. In this case, as the story unfolds, readers comprehend more and more just how black the narrator's heart is. Despite the cruel things he has done, he cannot find it in himself to feel true remorse or to take full responsibility for his actions. The man is a dire sociopath, and a black cat can be a fitting symbol for him.

Another symbolic interpretation of a black cat is of a warning. According to superstition, if a black cat crosses one's path, some type of danger will follow. In the story, the black cats provide warning of the rapid descent the narrator is taking into violence, a descent which culminates in the murder of his wife. Although the narrator has never heeded warnings and so continues on his precipitous path, the cat ends up warning the policemen about him, and they are able to arrest him and charge him with murder before he can harm any more people or animals with his sociopathic actions.