In the early 1950's, racial segregation in public schools was the norm across America. Although all the schools in a given district were supposed to be equal, most black schools were far inferior to their white counterparts.
In Topeka, Kansas, a black third-grader named Linda Brown had to walk one mile through a railroad switchyard to get to her black elementary school, even though a white elementary school was only seven blocks away. Linda's father, Oliver Brown, tried to enroll her in the white elementary school, but the principal of the school refused. Brown went to McKinley Burnett, the head of Topeka's branch of the National Association for the Advancement of Colored People (NAACP) and asked for help. The NAACP was eager to assist the Browns, as it had long wanted to challenge segregation in public schools. With Brown's complaint, it had "the right plaintiff at the right time."  Other black parents joined Brown, and, in 1951, the NAACP requested an injunction that would forbid the segregation of Topeka's public schools. 
The U.S. District Court for the District of Kansas heard Brown's case from June 25-26, 1951. At the trial, the NAACP argued that segregated schools sent the message to black children that they were inferior to whites; therefore, the schools were inherently unequal. One of the expert witnesses, Dr. Hugh W. Speer, testified that:
"...if the colored children are denied the experience in school of associating with white children, who represent 90 percent of our national society in which these colored children must live, then the colored child's curriculum is being greatly curtailed. The Topeka curriculum or any school curriculum cannot be equal under segregation." 
The Board of Education's defense was that, because segregation in Topeka and elsewhere pervaded many other aspects of life, segregated schools simply prepared black children for the segregation they would face during adulthood. The board also argued that segregated schools were not neccessarily harmful to black children; great African Americans such as Frederick Douglass, Booker T. Washington, and George Washington Carver had overcome more than just segregated schools to achieve what they achieved. 
The request for an injunction put the court in a difficult decision. On the one hand, the judges agreed with the expert witnesses; in their decision, they wrote:
Segregation of white and colored children in public schools has a detrimental effect upon the colored children...A sense of inferiority affects the motivation of a child to learn. 
On the other hand, the precedent of Plessy v. Ferguson allowed separate but equal school systems for blacks and whites, and no Supreme Court ruling had overturned Plessy yet. Because of the precedent of Plessy, the court felt "compelled" to rule in favor of the Board of Education. 
Brown and the NAACP appealed to the Supreme Court on October 1, 1951 and their case was combined with other cases that challenged school segregation in South Carolina, Virginia, and Delaware. The Supreme Court first heard the case on December 9, 1952, but failed to reach a decision. In the reargument, heard from December 7-8, 1953, the Court requested that both sides discuss "the circumstances surrounding the adoption of the Fourteenth Amendment in 1868."  The reargument shed very little additional light on the issue. The Court had to make its decision based not on whether or not the authors of the Fourteenth Amendment had desegregated schools in mind when they wrote the amendment in 1868, but based on whether or not desegregated schools deprived black children of equal protection of the law when the case was decided, in 1954. 
On May 17, 1954, Chief Justice Earl Warren read the decision of the unanimous Court:
"We come then to the question presented: Does segregation of children in public schools solely on the basis of race, even though the physical facilities and other "tangible" factors may be equal, deprive the children of the minority group of equal educational opportunities? We believe that it does...We conclude that in the field of public education the doctrine of 'separate but equal' has no place. Separate educational facilities are inherently unequal. Therefore, we hold that the plaintiffs and others similarly situated for whom the actions have been brought are, by reason of the segregation complained of, deprived of the equal protection of the laws guaranteed by the Fourteenth Amendment. 
The Supreme Court struck down the "separate but equal" doctrine of Plessy for public education, ruled in favor of the plaintiffs, and required the desegregation of schools across America.
The Supreme Court's Brown v. Board of Education decision did not abolish segregation in other public areas, such as restaurants and restrooms, nor did it require desegregation of public schools by a specific time. It did, however, declare the permissive or mandatory segregation that existed in 21 states unconstitutional.  It was a giant step towards complete desegregation of public schools. Even partial desegregation of these schools, however, was still very far away, as would soon become apparent.