Final answer:
Giles Corey and Francis Nurse arrive at the Proctor household to seek help in freeing their wives, Martha Corey and Rebecca Nurse, who were imprisoned due to the Salem witch trials.
Step-by-step explanation:
Giles Corey and Francis Nurse arrive at the Proctor household in Arthur Miller's play The Crucible due to the escalating witch trials in Salem. They are concerned about the accusations made against their wives, Martha Corey and Rebecca Nurse, and are seeking help to free them from prison. The gravity of the situation and the injustice they feel are driving factors in their visit, as they are desperate to clear their wives' names and stop the hysteria that has engulfed the town.