What is this method used in the "it's not your fault" segment of Good Will Hunting and why does it work? I mean the "it's not your fault" part at the end of this movie segment. Could anybody explain this method and why it works? 

What happens if the psychologist didn't get any reaction (like crying) from the case (Will), doesn't he look like a jerk repeating the same words 9 times?
An addition to the other answers:

We must remember that we are watching a movie. Movies are often called "dramatizations", a term that makes very clear what this type of movie does: it creates drama. It was not made to educate the viewers about how a therapy works, but rather to evoke intense emotions in the viewers. We should even assume that this movie does not faithfully depict any actual therapy but rather takes up the ideas that most viewers have of what would be helpful and reflects them back at them, because reinforcing a belief that you already hold will create the strongest emotional echo.

What do most people do in a situation like that in the movie? They tell their friend that "it is not your fault". Most therapists don't do that. Telling a patient how he or she should feel often has adverse effects: the person begins to defend his or her emotions from the devaluing judgment that they perceive the therapist's suggestion to be. What happens is that the belief in their own guilt gets cemented and harder to overcome.

A good therapists helps a patient to arrive at the conclusion by themselves. The most powerful ideas, when it comes to changing yourself, are those insights that you have yourself. A therapist might use questions ("Why do you think ...?") or careful suggestions ("Do you think it is possible that ...?") to direct the thinking of the patient, or the example of himself or a group of other patients with similar experiences (in a group therapy). Another component is psychoeducation, i.e. explaining to the patient that feelings of guilt are common symptoms and why patients experience them.

I cannot view the video, so my examples probably don't fit the situation at hand. Please always provide a short summary.