King addresses both black people and white people in his "I Have a Dream Speech." He tells white people that for a hundred years they have been promising black people equal access to the American dream as long as they patiently wait a little longer. Dr. King says the time of waiting is over. It is time for society to pay black people what it is has promised them. Dr. King says he worries that trouble will erupt if blacks are kept waiting much longer, stating:

Those who hope that the Negro needed to blow off steam and will now be content will have a rude awakening if the nation returns to business as usual.

However, he then turns to his black listeners and says, in the line I believe you are referring to:

We must not allow our creative protest to degenerate into physical violence.

King knows the black community is ready to explode violently. However, he does not want this to happen; he calls for non-violent action as the route to civil rights.

This is completely consistent with King's longstanding belief in non-violence. He says:

Again and again we must rise to the majestic heights of meeting physical force with soul force.

In speaking of soul force, King is alluding to the theories of Gandhi, on whose non-violent liberation of India from British rule he modeled the civil rights movement. Gandhi believed in soul force, or satyagraha, which is the power of standing firmly in the truth. King taught his followers the principles of non-violence, but acknowledged how difficult it can be to not retaliate violently against violence. He is reminding his followers in this speech that peaceful protest is at the core of how they will successfully win their rights.