He is appealing to Fortunato's pride. Montresor has an elaborate plan for revenge against Fortunato, but the audience is never made aware of the exact nature of the grievance. His entire plot centers around luring Fortunato into his family catacombs, deep beneath the city.
When Montresor finds Fortunato, he is already fabulously drunk. Montresor encourages this, both by promising Amontillado (a famous wine) and providing Fortunato with alcohol on their journey. With each drink, Fortunato becomes less and less capable of rational thinking, and is easily swayed by Montresor's suggestions.
Adding to this drunkeness, Montresor continually flatters Fortunato, betting on his pride to draw him further into the depths. He mentions a rival of Fortunato, Luchesi, and says he will consult him if Fortunato is not interested. Fortunato refuses to allow this to happen, and so he follows Montresor, although increasingly against his better judgment. Thus, this combination of inebriation and appeal to pride allows Montresor to trap his victim.