I believe the non-violent movements of the 50s and 60s were a fantastic--albeit hard won--lesson for our society. There are many lessons to be learned from these movements, but three in particular stand out for me.
First, it showed that the acts of small groups can make a difference. Fighting segregation in the political and social environment of the 50s must have seemed an obstacle that was overwhelmingly insurmountable. Against the entrenched politicians and law enforcement in the south, resistance truly must have seemed a futile act. Despite this, these students decided that it would be better to try and fail than to accept an unjust fate--even when failure must have seemed inevitable and the price for resistance severe.
Second, it showed the power of a non-violent movement to unite a community behind its cause when combated with violence and injustice. I believe that the fuel behind the success of this movement was the persistence in maintaining non-violent practices in the face of violent resistance. The very act of responding to these protests with violent actions provided credibility and support for the movement, especially when the protesters refused to relinquish their resolve to continue and also refused to respond in kind. This sparked a flame of resistance in many who may have otherwise remained bystanders--perhaps even President Kennedy. As Martin Luther King said when addressing a congregation of Alabama civil-rights activists besieged by an angry mob threatening to do them harm, "Maybe it takes something like this for the Federal Government to see that Alabama is not going to place any limit upon its self, it must be imposed from without."
Near the end of the movie one of the former-protesters was telling a story about an experience he had while in prison. He said that a man was ordered to beat him as punishment for refusing to allow his mattress to be taken away. The prisoner looked into the eyes of his punisher and saw pain, and knew it to be greater than his own. Therein lies the greatest lesson of non-violence. Anyone can lash out with physical force in an attempt to impose their will on others. Its easy; instinctual, even. It takes a much stronger will to restrain this temptation; stronger still to do so in the face of violence. The pain of the punisher was that of recognition; recognition of his own weakness when confronted with true strength.