The story begins with the sentence: "The thousand injuries of Fortunato I had borne as I best could, but when he ventured upon insult I vowed revenge." It is highly unlikely that the narrator has actually been "injured" in any way by Fortunato a thousand (1000) times. He merely means by this remark that Fortunato had "injured" him--in what ways, he does not say--more times than he can count.
The use of hyperbole (an exaggerated statement meant to emphasize the importance and severity of the writer's claim, often enticing you to join his side of the argument) in this case manages to make us--his readers, his audience--accept that Fortunato has wronged him grievously and at the same time is so overstated that we are not inclined to ask for details or examples. We are given an immediate impression of a Fortunato who is not a gracious nobleman so much as a rich man who wantonly insults others and cares not for their feelings.
The effectiveness of this device makes us accomplices in the narrator's eventual crime. We learn too late that he is an unreliable narrator--although the hyperbole should have clued us in--and have accepted as gospel the words of a madman.