The march (it might be better to say "marches" since there were various attempts) from Selma to Montgomery in 1965 worked to win more white sympathy for the Civil Rights Movement and to increase the confidence of those who were participating in the movement.
The marches gave greater confidence to the people (most of whom were black) in the movement. They saw just how powerful they could be if they were determined enough. They were able, through nonviolent action, to defeat some of the most hardened resistance to their cause. This gave them a greater sense of accomplishment and of power.
The marches tended to make white Americans more sympathetic to the cause of civil rights. Some of the pictures and video from these marches are among the most famous of the Civil Rights Movement. These images made many whites take the side of the movement as they saw what was being done to people who were asking only for the right to vote.