Quasimodo is the hunchback from Victor Hugo's The Hunchback of Notre Dame. He is an ugly, deformed bellringer of the cathedral in Notre Dame. He also becomes deaf because he is always around the loud ringing of the bells. He is devoted to Esmeralda, a gypsy dancer on trial for witchcraft. He tries to save her from the scheming Archdeacon named Frollo (who also is the one who raised Quasimodo when he found him as an infant). Through Frollo's efforts, Esmeralda is finally hanged. At her death, Quasimodo throws Frollo from the top of the bell tower. Years later, the skeletons of a woman and a misshapen man are found together in Montfaucon, the criminals' burial vault.
Quasimodo is a tragic protagonist, and a type of noble savage. Though his story is a sad one, he is a pretty commonly used allusion for humorous means.
Basically, whenever you see someone or something awfully deformed, you might refer to them as Quasimodo--or in light of Quasimodo--as a sort of cruel joke or mockery. ("Hey! That must be Quasimodo's dog!" Or when you see someone in the morning before they've had time to get cleaned, groomed, and ready: "Hey, it's Quasimodo!") The fact that "Quasimodo" is fun to say and humorous to the ear encourages this sort of usage.
Quasimodo's story was made into a Disney Movie in 1996. Regrettably, I haven't seen it yet.
And now for a bit of Allusion trivia, can any of you tell me which Adam Sandler movie makes a reference to Quasimodo?