This story is set during the Spanish Inquisition, which was a bloody period of history where people who wouldn't convert to the Catholic church were rounded up, tortured, imprisoned, killed, and put on trial for being heretics. So, to infer from that information, and from what the narrator says in his dazed state, we have to guess that he has refused to join the Catholic church and has so been brought before judges to pronounce his sentence. Joining was required, you see, and if you didn't, you had to be punished. People were "punished" for a lot of other things, too, but, that was the main one. So, the narrator was a man who refused to do what they wanted him to do. The judges were the ones who were going to decide what his fate would be: imprisonment, torture, or death.
As it turns out, they punish him in all three ways--they throw him in a dark prison, torture him in phases, and intend on killing him towards the end. Not a very fun fate, to be sure. I hope that helped with this question--for your other questions, try submitting them separately on other days, as the format for this website indicate only one per day. Good luck!
In the short story 'The Pit and the Pendulum' by Edgar Allen Poe, his captors are referred to only by the anonymous 'they' in the first sentence where he is talking about how he was untied ready for his 'court' appearnace. He appears to faint at the final pronouncement of the death sentence. He then refers to people as 'inquisitors:'
'the sound of the inquisitorial voices seemed merged in one dreamy indeterminate hum.'
so it seems safe to assume that he has been tried and found guilty of heresy by the judges of the Inquisition. He seems petrified of them, describing them as white-lipped (presumably with anger) and wearing black robes. They give out an aura of unforgiving contempt and complete disregard for the ethics of human torture. No wonder he was afraid for the brutality and cruelty of these punishments were notorious - in Mexico for example victims were hanged or burned at the stake.
The narrator of the The Pit and the Pendulum has been sentenced for his religious beliefs. He lives during a time when a government, a Catholic government, imposed an inquistion. Even though the government was Catholic, heretic Catholics and Protestants were persecuted and sentenced to death. Hence, the narrator is standing before judges.