It hit me the most clearly during a rewatch of Iron Man, and since I did a post on Captain America last week, I decided to do an Iron Man post today. And maybe next week I'll do Thor. Because it's Marvel and because I can.
This point usually falls somewhere during the second half of the story--generally in the part right after the midpoint that Blake Snyder calls "The Bad Guys Close In." It comes just before and directly affects the "All Is Lost" point when the hero hits his lowest of lows.
Up to this "moment of self doubt" the hero probably hasn't questioned his cause or his goals at all. The idea that they could possibly be at fault hasn't even occurred to him.
And then something happens that comes at the hero from a side wind. To him it seems completely out of the blue and it forces him to question everything he's done or tried to do from the beginning of the story right up to that present moment.
His reaction will be something like this:
Tony Stark starts out as an egocentric arms manufacturer who makes speeches about how awesome weapons are. That all changes at the catalyst point when Stark watches fellow Americans get shot with his guns and is himself almost killed by one of his own missiles. He goes home with a new mission: Stark Industries is no longer going to make weapons.
Unsurprisingly, he gets a lot of flak for his decision, especially from his friend and mentor, Obadiah Stane. But other peoples' opinions don't affect Stark much; not even getting kicked off the board of directors of his own company can faze him--that is, until Stane reveals that he was the one who voted Stark out.
This revelation comes at a fairly low point for Stark. He had to show up uninvited to his own charity ball and he ends the night with a guilt trip over his terrible treatment of his secretary, Pepper Potts. These things got his attention, and Stane's confession comes like a slap in the face. Stane explains he did it to protect Stark--to shield Stark from the consequences of his own folly. Suddenly Stark isn't so sure whether he's a hero on a white horse or a total jerk who's ruining his company and hurting his friends.
The realisation leaves him looking like this:
Forcing the hero to question his cause also forces him to question himself. It shifts the focus of the story from the smaller issue of "Will the hero triumph?" to the much larger and more relevant issue of "Will good triumph?"
And it makes us, the viewers, question the truth of the premise. Is peace achievable, or is it a delusion? Can saving lives be more important than running a successful company? We started out assuming the answer was yes, but once that assumption is questioned we realise that we want the answer to be yes.
The moment of self doubt drives home the message of the story, which is why it's so powerful, even though it may only be a few sentences or a few lines of dialogue. Make your hero face those tough questions and make your readers face them too.