Final answer:
Winston and Julia visit O'Brien's apartment to join the Brotherhood, as they perceive O'Brien as a rebel against the Party in Orwell's '1984'.
Step-by-step explanation:
Winston and Julia go to O'Brien's apartment because they believe him to be a member of the Brotherhood, the rebel group opposed to the Party in George Orwell's novel, '1984'. They are seeking to join the clandestine resistance against the oppressive regime.
O'Brien has cunningly cultivated an aura of dissidence and has extended an invitation that seems to indicate his rebel sympathies, prompting Winston and Julia to take the risky step of visiting him at his home.