Hyperbole is an exaggerated statement or claim that is not meant to be taken literally. One of my favorite hyperbole phrases is from the movie "The Sandlot." The character "Smalls" doesn't understand a lot of the baseball slang. His lack of knowledge is always surprising "Ham" Porter. Porter's response is always "You're killing me, Smalls!" Of course Smalls is not actually killing Porter. It's hyperbole.
In Poe's "The Cask of Amontillado" the opening line is as follows:
"THE thousand injuries of Fortunato I had borne as I best could; but when he ventured upon insult, I vowed revenge. "
Montressor is likely exaggerating the exact number of injuries done to him by Fortunato. At one injury per day, that would have taken Fortunato 2.74 years to give Montressor that many injuries. That assumes that the two men saw each other every day. If they saw each once per week, that many injuries would have taken over 19 years. Montressor is using hyperbole to stress his point that Fortunato has injured him a lot.
Hyperbole is a term for the kind of figurative language in which the speaker extravagantly exaggerates for the sake of emphasis. It is derived from the Greek word for "over-casting."
Edgar Allan Poe's short story "The Cask of Amontillado" opens with the use of hyperbole when the narrator of the tale, Montressor, claims, "The thousand injuries of Fortunato I had borne as best I could; but when he ventured upon insult, I vowed revenge." Montressor is clearly exaggerating about how many times Fortunato has insulted or offended him, but is doing so to emphasize how seriously he has taken the number of offenses which actually did occur. This sets the reader up to understand that Montressor is unreliable and overdramatic in his assessment of others.