Greed is a selfish desire for something. One can be greedy for power, money, food, respect, and so on. Most importantly in this story, Fortunato has immense greed for the respect of others. Montresor knows this and uses it to his advantage. Early in the story, he notes that Fortunato's "weak point" is how proud he is of his knowledge of wine. When Montresor meets Fortunato during the carnival, he notes that Fortunato "had been drinking much." So, Fortunato also shows his greed for wine itself.
He uses Fortunato's pride to lure him into his wine vaults. This is another moment when Fortunato's greed for respect shows itself. Montresor tells Fortunato that he is uncertain about an amontillado he has just bought. He tells Fortunato not to worry about it and that he will ask his other friend, Luchesi. Fortunato must protect his reputation as a wine aficionado, so he insists on being the one to test the amontillado.
As they descend into the vaults, Montresor continues offering Fortunato wine and he accepts every time. First, he offers Medoc and then De Grave, clearly an example of foreshadowing. Montresor adds, "He emptied it at a breath. His eyes flashed with a fierce light. He laughed and threw the bottle upward with a gesticulation I did not understand."
His greed for wine and his greed for the respect of being known as the most knowledgeable connoisseur of wine are Fortunato's two main flaws. Montresor uses these to flaws to lead Fortunato to his demise.