We know that it's only a matter of time until Big Brother catches Winston, but what we don't know is what the Party will do to him, how they'll do it, and to what extent they'll do it. The climax is when we learn that they want more than just confessions and death from the people they catch. The Party wants complete and total belief and the love of those who are rebellious. Therefore, the climax occurs when Winston gives in and admits "he loved Big Brother".
Julia had previously told Winston that Big Brother couldn't get "inside" a person, but we learn by the end that they can control every part of a person, inside and out. It's not enough that Winston agrees that "two and two make five"; he has to also profess his love for Big Brother. Once he does that, we see Winston's shell of his former self. His hair and teeth are gone, his body's destroyed, he's given a meaningless job, and then he becomes an alcoholic. This is all necessary in order for Oceania to live up to its philosophy: "WAR IS PEACE. FREEDOM IS SLAVERY. IGNORANCE IS STRENGTH."