To answer this question, we might attempt to articulate John Proctor's decision, looking at his character, his values, and what he thinks is worth dying for.
Facing his death, John Proctor is forced to reflect on who he is. He berates himself for his weakness, having already admitted to his adultery with Abigail. Elizabeth disagrees with Proctor's low assessment of himself, telling her husband that he is a good man.
At this point, Proctor revives the core values that define him as a character: strength of will, honesty, and integrity.
He is at his most self-aware in his final speech when he realizes the importance of maintaining his integrity.
The choice that he faces when he is being pressed to sign a false confession can be seen as the choice to die to these values or to live without them. Should Proctor choose to live, he will be choosing to betray his values, compromise his integrity and also betray several of his neighbors.
Proctor chooses to die. He is willing to die for these values and willing to do to remain "himself".
Proctor's final recantation of his confession and his refusal to put his principles aside to save his life, we see the triumph of personal integrity in a world of moral uncertainty.