The climax of The Hunger Games is during the would-be double suicide of Katniss and Peeta. Previously, the Gamekeepers had announced that there could be two victors if they were from the same district. Since Katniss and Peeta are both from District 12, they believe they both can live if they are the last two tributes left standing. In reality, the Gamekeepers announced this rule change to get the two to pair off during the competition, leading to a better show for the viewers.
This rule change was a lie. It is later announced that there can only be one victor. Katniss has a stroke of genius at this point: if she and Peeta, two star-crossed lovers, were to commit suicide, the Gamekeepers would be in quite a predicament, as they would have no victor.
Without a victor, the whole thing would blow up in the Gamemakers' faces. They'd have failed the Capitol. Might possibly even be executed, slowly and painfully while the cameras broadcast it to every screen in the country.
If Peeta and I were both to die, or they thought we were . . .
This leads to the climax—when Katniss acts as if she is eating the berries, telling Peeta to trust her. The readers are left on tenterhooks, not knowing whether the tributes from District 12 will live or die. At the last minute, the Gamekeepers decide to go back to the rule that allowed two winners, and Katniss and Peeta become the victors, winning the Hunger Games.