The heart of civil disobedience is refusing to obey an unjust law, and hence forcing the state to openly display the violence that is inherent in the unjust law. Ultimately the point of the act of civil disobedience is to force the state to use force against you to make you comply, and so highlight the yawning gap between law and objective justice which you believe to exist. This was the genius of Gandhi's nonviolent resistance, in which his supporters gladly marched into beatings because they knew that by so immolating themselves they could eventually win over the opinion of their oppressors, who tired of killing innocent men much more quickly than they would have tired of overseeing people who were passive in the face of the laws.
Civil disobedience hence presupposes a system that is open to change and able to be influenced, and it works best when public opinion can be swayed to pity the plight of the oppressed. I could demonstrate my disobedience to the law against murder by killing a man, but I am unlikely to arouse sympathy; and civil disobedience usually distinguishes itself from activism in that it involves me refusing to discharge an unfair obligation, such as the draft, rather than actively seeking rules to break that I could just as easily leave unbroken.
The ultimate genius of civil disobedience lies in the fact that the individual carrying it out is presumably of some use to the oppressor, but he robs the latter of his own usefulness by the act of disobedience. To take the example of the British in India, the natives were of use to the British because they allowed them to glory in the extent of their dominions and derive economic and military benefits from them; but by refusing to live as slaves and instead sacrificing their own lives, Gandhi's men robbed the British of the prize of ruling over them. After all, no-one can derive benefit from ruling dead men. However, one can only imagine what would have happened if the Jews had decided to use such tactics to contest the Nazis on a large scale, which is yet another reason that their regime is viewed as having constituted a unique evil.
Civil disobedience is a potent form of power under the right conditions because it can stand up so readily against violence. It cannot beat violence in a pitched battle, but it does not have to precisely because it robs violence of its legitimacy. It takes a unique and rare evil to inflict violence on a massive scale against a people who do not fight back, but merely consent to have it inflicted on them; and such an evil is much rarer in this world than the common, banal oppression that lies behind the routine enforcement of unjust laws. For the oppressed, non-violent civil disobedience is a force multiplier, a way to remain right in the eyes of their contemporaries and history by giving all they have and taking nothing but punishment. Such a profound human capacity has so rarely been expressed fully that every story of it still touches us.