In the opening paragraph of Edgar Allan Poe's short story "The Black Cat," the narrator states that his "immediate purpose is to place before the world ... a series of mere household events." In other words, he wishes to explain to the world a series of events that occurred in his household. His reason for wanting to do so is stated in the sentence prior, to "unburthen [his] soul," meaning to unburden his soul, or to relieve his soul by revealing something that has troubled his soul. By the end of the first paragraph, he says that he intends to explain a "succession of very natural causes and effects." Hence, the narrator is saying his purpose is to relieve his soul by explaining a series of household events based on their causes and effects. It's his reference to causes and effects that is the most interesting, for it's the causes and effects that directly tie to the most dominant theme in the story.
The most central theme in the story is the dual side of human nature--good and evil--and what causes will bring out one side of human nature as opposed to the other. The narrator uses the second paragraph to explain how gentle and tenderhearted he has been all his life, starting from childhood and continuing into manhood. His tenderheartedness was especially reflected in his love for vulnerable animals. Yet, he also later explains that after getting married, his "temperament and character" began to change as a result of the "Fiend Intemperance." The word fiend means devil or demon; the word intemperance can be defined as an "excessive or immoderate indulgence in" alcohol (Random House Dictionary, 2015). In other words, the narrator is explaining that his character significantly changed because he became an alcoholic. Furthermore, the cause alcoholism led to the disastrous effects of the cruelty he demonstrated through his murderous acts, which he is soon to be executed for.
Hence, all in all, the narrator is stating that his purpose is to explain how a cause like alcoholism can lead to the effect of changing a good human nature into an evil one, or unleashing the evil nature that lies hidden beneath the good nature.