The carnival at which the narrator, Montresor, meets Fortunato is occurring "during the supreme madness of the carnival season."
The "carnival season" is the period of time preceding Lent, the Christian period of preparation for marking the death of Jesus on Good Friday. During Lent, particularly in predominantly Roman Catholic countries such as Italy (where "The Cask of Amontillado" presumably takes place), believers are expected to make sacrifices in their lives in remembrance of Jesus's sacrifice. This includes giving up meat, eggs, and other foods or beverages, and activities that appear too boisterous and celebratory during the time of preparation to mark Good Friday and Jesus's death.
Carnival season is the time prior to Lent. It is a time to celebrate and party before such activities need to cease; a time to use up the alcoholic beverages and rich foods that will be banned during Lent; a time to use costumes to hide one's identity while indulging all the fantasies that will be forbidden soon.
Many words could describe the mood of the carnival. Uninhibited, celebratory, excited, flamboyant, unrestrained - take your pick.
When the narrator says that he encountered Fortunato during the "supreme madness" of the carnival, he is conveying important bits of information. One is that Fortunato is drunk. Poe writes: "He accosted me with excessive warmth, for he had been drinking much." Everybody is drunk during the supreme madness of a big carnival--except for Montresor himself, who is cold sober. Another bit of information suggested by the descriptive words "supreme madness" is that Montresor is going to have an extremely difficult task of leading Fortunato away from the mob to his palazzo without being recognized. Montresor certainly doesn't want people to remember that the last person seen with Fortunato on the night he disappeared was himself. Poe provides Fortunato with the most conspicuous possible costume, a jester's motley complete with a cap with jingling bells. Fortunato is sure to attract attention, but Montresor knows this will attract attentionawayfrom himself. All anyone will remember would be that Fortunato was accompanied by a man in a black cloak wearing a black mask. He could have been anybody. Getting Fortunato down into his catacombs is Montresor's main problem, and hence it is the main conflict in the story. The drama in the story is created by the logistical problems involved in getting Fortunato into the catacombs, leading him to the niche, wrapping the short chains about him, and locking the padlock. The fact that Fortunato is drunk makes it easier and at the same time harder. It is not easy to handle a large, boisterous, drunken man, especially in the darkness, although it is fairly easy to deceive a man in such condition.
The word "madness" seems to express the mood of the carnival better than any other adjective. If two words were permitted, they would be "supreme madness." Poe does not specify where this carnival is taking place, but there are many indications that it must be in Venice. For one thing, the Carnival of Venice is world-famous. It would have to be taking place in a big Italian city to justify the description of the event. Furthermore, the word "palazzo" is used several times. Venice is full of palazzi, many of them hundreds of years old, and it would have to be an important city to contain palaces. Both Montresor and Fortunato live in palazzi. The city would have to be one that does considerable importing and exporting. The cask of amontillado, if it had existed, would have had to come in by ship from Spain. Montresor states that they are under the river towards the end of their underground journey. This would have been, suggestively, the Po River which runs through the rich Po Valley and terminates near Venice.