The narrator begins his story by speaking of his sentence of death. The narrator then notes how he recalls the "inquisitorial" voices who convicted and sentenced him. The adjective "inquisitorial" indicates a reference to the Spanish Inquisition. The Spanish Inquisition was a particular part of a broad movement to enforce Catholic doctrine and influence; part of this enforcement required Catholic monarchs to find, suppress, and sometimes banish, torture or kill heretics (those who did not follow the Catholic faith). 

Later in the story, the narrator refers to the "Inquisition" and the reference to the Spanish Inquisition becomes more clear: 

And the death just avoided was of that very character which I had regarded as fabulous and frivolous in the tales respecting the Inquisition. To the victims of its tyranny, there was the choice of death with its direst physical agonies, or death with its most hideous moral horrors. 

So, the narrator is one of these victims of the Spanish Inquisition. Evidently, he was accused of heresy and imprisoned in this dungeon. His sentence was death but that death was to be preceded by psychological and physical torture. The dungeon itself is in total darkness with the pit in the center which the narrator narrowly avoids falling into. Part of his psychological torture was to place him in an utterly dark dungeon with a pit that he could not see. Having avoided falling into the pit, the narrator was then subjected to the pendulum.