The story starts with this quote:
"The thousand injuries of Fortunato I had borne as I best could, but when he ventured upon insult I vowed revenge."
At the end of the story, Monstresor tells us this:
"For the half of a century no mortal has disturbed them."
Thus, Monstresor starts by making sure we understand that Fortunato is the one to precipitate the need for any action. He ends by telling us that it has been 50 years since this happened. We can assume this is the first telling of this story in those 50 years. So why is Monstresor telling the story now, and to whom? He addresses his audience specifically:
You, who so well know the nature of my soul, will not suppose, however, that I gave utterance to a threat.
Whomever his audience is knows his soul well. These two pieces of information - the time passage and the address to his audience - have caused many critics to assume that Monstresor is confessing upon his deathbed. He was clearly a man of adult years, probably in his 30s or 40s at least to have such a home as he does. Add 50 years, and it is likely he would be on the verge of dying. He wants to confess, but in confessing, he wants his action to seem not like cold-blooded murder, but rather a rational response to an injury sustained at the hands of Fortunato. Montresor never specifies the injury, and we can see that Poe is showing us not a story of justified revenge, but of a man's anger and the drive to commit murder, similar to the justification given by the narrator of Tell-Tale Heart.
Thus, the words above are all intended to underscore Monstresor's desire to establish his innocence. He cannot be responsible because Fortunato brought is upon himself. He, Monstresor, must be absolved on this crime.