What is the relationship between the Civil Rights Movement and Brown vs. Board of Education?

Brown vs. the Board of Education of Topeka, Kansas (1955) was the first Supreme Court case to most effectively work toward dismantling de jure, or legal segregation in public school systems. This case would also lead to efforts to desegregate lunch counters and other public accommodations throughout the South. 

Brown vs. the Board was not the first attempt of civil rights leaders to address Jim Crow laws. A. Philip Randolph helped to lead efforts to desegregate public transportation. In 1955, the Interstate Commerce Commission ruled that all segregation on interstate buses and trains had to end by January 10, 1956. Some Southern states reluctantly complied, while others tried to circumvent the law by upholding separate waiting rooms for intrastate black passengers.

There was resistance, too, after the Warren Court decided the Brown case. A separate decision in 1956 was handed down to deal explicitly with how Southern states should handle the desegregation of schools. 

Many states were slow to comply. Citizens were resistant. Consider the mayhem in Little Rock, Arkansas in 1957 when a public high school was desegregated. Consider, too, how little Ruby Bridges had to be escorted to elementary school by a federal marshal in New Orleans. 

It is important to remember that schools and public transportation were merely the first efforts. The goal of Thurgood Marshall, Daisy Bates, and others who assisted in the early efforts, was to dismantle Jim Crow permanently. 

One can argue that, by seeing the hatred demonstrated toward children merely attending school, and the distress those children suffered, more Americans began to see the urgency of equality. Thus, people from all over the country, of all races, began to participate in efforts to desegregate lunch counters; university students began to protest their schools' complicity in black oppression; and organizations and their legal advisers worked to end discrimination and segregation in federal employment. 

These efforts would lead to the official act to end legal segregation throughout the nation: the Civil Rights Act of 1964. The Civil Rights Act made it illegal and unconstitutional for any public institution or place of accommodation to discriminate or bar admission on the basis of race. This was followed by the Civil Rights Act of 1965 which made it illegal for Southern states to bar blacks from voting, particularly with its persistent use of poll taxes and tests which were not required of white voters.