"They had done it. They had done it at last!" What had Winston and Julia achieved?
As was mentioned in the previous post, the given quote takes place at the beginning of Book Two, Chapter 8. In Chapter 8, Winston and Julia finally meet privately with O'Brien, who they assume is a member of the Brotherhood. Access into the home of an Inner Party member is rare and nearly impossible, which is one reason why their visit is an extraordinary achievement. Winston and Julia are also excited about joining forces with a Party dissident. They both recognize the risk involved in joining an organization like the Brotherhood, and meeting with O'Brien about rebellious activity is dangerous. Avoiding the constant surveillance and "outwitting" the Party is also considered an impossible task. Winston and Julia both believe they have deceived the Party and are on their way to becoming members of the Brotherhood that will undermine the government. Unfortunately, O'Brien is a zealous Party member who fools Winston and ends up torturing him.
The line you cite is the very first line of Part 2, Chapter 8.
In this chapter, Winston and Julia have, at last, managed to get themselves into a meeting of what they think is the Brotherhood. They have been invited to a meeting at the home of O'Brien. At this meeting, the will end up hearing what they think are the secrets of the Brotherhood and they will be asked to swear oaths to do various things the organization demands.
So they think they have triumphed, but really, they have doomed themselves further because O'Brien is not really a dissident.