This is a question that has never been answered to everyone's satisfaction. Some readers have assumed that Montresor is making a verbal confession to a priest. One reader suggested that Montresor might be confiding in a grandson. My own opinion is that the "You" is an old male or female friend to whom Montresor is writing a letter. This literary device enables Poe to avoid a lot of exposition. The device enables Montresor to assume that the recipient of his letters already knows a great deal about him, including what he does for a living. After all, Montresor is making this disclosure fifty years after the fact, so it would appear that he has known this confidant, or confidante, for at least fifty years. It seems to me that the story should be taken as a translation of a letter that fell into the hands of an American editor named Edgar Allan Poe, who translated into English, either from the French or Italian, and published it in a ladies' magazine. Montresor could have sent the letter to the confidant, or confidante (my impression is that the recipient was a woman), and it was found among that person's papers upon his or her death. Another scenario might be that Montresor wrote a letter to this old friend one night when he was drunk and then decided not to send it when he read it over the next morning. Many of us have done something along these lines, haven't we? But Montresor didn't destroy the letter, and it was found among his own papers after he died.
Poe does something similar in his "Ms. Found in a Bottle." That story is putatively a transcription of a manuscript which a desperate man put in a bottle and tossed overboard during a howling storm. "The Cask of Amontillado" might have been improved if Poe had at least indicated the identity of the person to whom the letter was sent--or not sent. It raises questions which do not seem to help the story. What is really important in appreciating the story is not in trying to deduce the identity of the person to whom it is being narrated as it is to understand Poe's purpose for using this anonymous interlocutor in the first place. What would be the effect of telling the story without pretending it is being told to some single individual? It seems that it would make the story read like an open confession to the world of Montresor's guilt. Why would he do that after keeping his secret for fifty years? It would be foolhardy. We can at least admire Montresor for being able to pull off the perfect crime and achieve the perfect revenge. But if he broadcast his guilt to the whole world in a moment of madness, we would lose all regard for him. A perfect crime is only perfect if nobody ever finds out whodunit. That seems to be a problem with writing a perfect-crime story. How can it be perfect if all of us readers know the identity of the perpetrator? Poe himself gives his recipe for a perfect crime at the beginning of the story.
THE THOUSAND INJURIES of Fortunato I had borne as I best could, but when he ventured upon insult I vowed revenge. You, who so well know the nature of my soul, will not suppose, however, that I gave utterance to a threat. At length I would be avenged; this was a point definitely, settled—but the very definitiveness with which it was resolved precluded the idea of risk. I must not only punish but punish with impunity. A wrong is unredressed when retribution overtakes its redresser. It is equally unredressed when the avenger fails to make himself felt as such to him who has done the wrong.
He is obviously bragging about how successfully he carried out his plan for revenge. He does not seem to be confessing to any priest or seeking forgiveness. At the end of the story he makes the point that his plan was a complete success.
Against the new masonry I re-erected the old rampart of bones. For the half of a century no mortal has disturbed them. In pace requiescat!
He sounds triumphant. He cannot keep his triumph to himself. He has to share it with someone, so he decides to confide in the only person he thinks he can trust with his secret: You, who so well know the nature of my soul. Of course, we could read the story as if Montresor is personally addressing us! We are his old friend, the one who so well knows the nature of his soul. On the other hand, maybe there is no one he could ever trust, especially with such a dark and heavy secret. Maybe he is only addressing an imaginary friend, just as many people who keep diaries tend to think of the diary itself as a personal friend in whom they can confide anything. Each entry may begin with the words, "Dear Diary."
Poe wanted to write the story in the first person. But he did not want it to sound like a confession to the whole world, something like The Confessions of Jean-Jacques Rousseau or the confessions of the anonymous narrator of Poe's own "The Tell-Tale Heart." So Poe created the fiction that his story was a confidential disclosure to a single individual either verbally and in person or else in the form of a letter. My guess is that it was supposed to be a confidential letter that was so confidential it was never even sent.