The very initial situation, or the initial source of the conflict, is that Fortunato and Montressor have a long history with each other. They have been rude to each other and hurt each other for a long time over many years. We don't exactly know the details, but we know that they are certainly NOT friends.
Montressor decides that if he can lure Fortunato into saying something rude about him, perhaps they can be done with their fighting forever--literally. So, when Fortunato follows him down into the catacombs, Montressor jumps at his opportunity. They are bickering back and forth when Montressor brings up the topic of Luchesi--and this sets them both off.
Fortunato calls Luchesi and ignoramus and Montressor believes this is his chance! He chains Fortunato inside a casket and slowly builds a brick wall around the casket so that Fortunato will suffocate to death. In this way, we know that the conflict has ended forever and that Fortunato knew exactly who was punishing him.