Montresor is an unreliable narrator in that he does not seem to be giving us the whole story and may be mentally unstable. However because it is from his point of view we know that Fortunado is doomed from the beginning, and can play along and follow the clues.
The impact of having Montressor telling this story is simple--without his thoughts and motivations being revealed, we have no story. Think about having a narrator with no access into his mind. Montressor lures Fortunato to the dungeon and walls him into an underground tomb, but we never know why. It seems insane, but we're just not sure.Even worse would be the story told from Fortunato's point of view. Then we'd be as clueless as he was about Montressor and his motivations and intentions.
Us being able to hear the story told through Montresor's eyes is key in this story; it creates all of the suspense, entertainment, and horror. The most important aspect of Montresor narrating is that we learn right off the bat that "I vowed revenge. You, who so well know the nature of my soul, will not suppose, however, that I gave utterance to a threat...I must not only punish but punish with impunity." Here we learn that first of all, Montresor would have his revenge; secondly, that he never uttered that intent out loud, and third that it would be merciless. This is key; because Montresor never spoke out loud his intent, if he wasn't the one narrating, we would have no idea that he intended revenge. We would be horribly bored as we read this super long story of a guy leading Fortunado to get some wine. It would be so boring in fact that most people probably would quit after the 3rd or 4th winding tunnel. We would think, "Who cares about these two dudes going to get wine? Get on with the story already!" But because we know that Montresor is planning some punitive revenge, we are kept on the edges of our seats, wondering over and over, what is he going to do? Where is he taking Fortunado?
Another thing to think about is that if we didn't have Montresor narrating, we would have no idea why he was patching poor Fortunado up in the walls of the catacombs. If we stuck with the story long enough to get to that part, we would think, "What in the heck is going on here? Why in the world is this guy killing his buddy?" Without the backstory given through Montresor where he refers to "the thousand injuries [and]...insult" of Fortunado, we would be clueless. So, we know why the cruel deed is being done. This makes it more satisfying and interesting.
The last impact it has is the horror level of being allowed into a villian's mind. Montresor is creepy. He is calculating, cold, mocking, insulting, callous, and takes supreme enjoyment from his task. He taunts Fortunado and his cough, and he, "that [he] might hearken to [Fortunado's suffering] with the more satisfaction,...ceased...labours and sat down upon the bones" to fully enjoy his victim's struggles. Getting inside the mind of a murderer is always a morbid fascination for people, and Poe tapped into that human interest quite successfully.