How did people summon the courage to confront the intimidation, brutality, and injustice they faced under the Jim Crow system?

Power has been unequally distributed throughout human history - there have always been rich and poor, royalty and peasantry, strong and weak, etc. Those in power shape the systems and structures that those not in power live by. Sometimes those systems are designed to ensure a healthy, equitable society, and sometimes they're designed to reinforce the existing power structures and keep as much power as possible concentrated to a select few. Jim Crow laws, which codified segregation in America in the late nineteenth and early twentieth centuries, are an example of the latter. Jim Crow laws made it more difficult for recently-freed slaves and their descendants to develop wealth, establish communities, and participate in the American educational, judicial, and political systems, which made it easier for the majority-white power structure to maintain control.
History has shown us that it is not impossible for those who suffer under unjust systems such as Jim Crow to generate positive and productive change and disrupt the control of those in power, however. The American labor movement, the women's suffrage movement, and even the American Revolution are examples of this, and they provided a map of sorts to Dr. Martin Luther King, Jr., Bayard Rustin, John Lewis, and other leaders of the American Civil Rights movement who worked to overturn Jim Crow. The common strategy employed by all of these movements was to meaningfully engage as much of their respective communities as possible in concerted, unified, strategic action against the systems that they were trying to change. While those in power source their courage and strength from the systems they've created, such as courts, militaries, and police forces, individuals in the Civil Rights movement and other similar movements got theirs from sheer numbers. The most effective change agents in such groups see the movement as bigger and more important than themselves, in the sense that its needs are more valuable than their own. When those in power intimidate or injure an individual, she or he has the courage to continue fighting because the movement continues to fight, and the movement is paramount.

The fight to end the segregation and injustice of the Jim Crow system was a long one. During the Civil Rights era, people summoned courage by forming grassroots organizations that were often formed at local churches. For example, the Montgomery Bus Boycott of 1955-56 was organized after Rosa Parks, an African American seamstress and member of the NAACP, refused to give up her seat in a white section of a segregated city bus in Montgomery, Alabama. The movement coalesced around a young preacher named Dr. Martin Luther King Jr., and meetings were held at his church. The leadership of the movement, along with the example of Rosa Parks, helped people summon courage, as King was a dynamic speaker who was able to rally the population of Montgomery to stay off the buses during the boycott. He was helped by a series of local organizers, and the leadership and grassroots nature of the movement helped provide people with courage and strength.