How does the beginning of The Pit and the Pendulum contribute to the meaning of the story?
The translation of the epigram at the beginning of the story is:
Here the wicked mob, unappeased, long cherished a hatred of innocent blood. Now that the fatherland is saved, and the cave of death demolished, where grim death has been, life and health appear.
The "wicked mob" is the Spanish Inquisition which was created to preach and enforce Catholic doctrine in Spain and the Spanish territories. The Inquisition became notorious for stories of how the leaders of the Inquisition tortured and executed "criminals" who did not follow or submit to their version of Catholic orthodoxy. In this epigram, Poe establishes their cruelty. The phrase "cherished a hatred of innocent blood" means the leaders of the Inquisition loved to hate innocent people. The indication is clear that the Inquisition's victims were mostly innocent people. The Inquisition's plan was to eradicate nonbelievers, thus leaving a society of spiritual "life and health."
In the opening paragraphs of the story, the narrator recalls being sentenced to death, but he is so groggy that he does not know or articulate exactly why he's been convicted. This is a result of his being tortured and/or drugged, but it also suggests he has done nothing to earn a death sentence. He does not recall or say what his crime is. The omission suggests its insignificance. Beyond the Inquisition's oppressive policies, was it even a real crime?
So, with the beginning of the story, we have a narrator who is sentenced to death and it is something he almost accepts as a relief. But then he takes us through his torturous ordeal. By starting with a death sentence, the reader gets a sense of an upcoming finality. But the narrator describes his torture and it seems to drag on. Poe does this to illustrate the narrator's agony as his ordeal is prolonged.