Brown II followed the 1954 Brown v. Board of Education which forced the desegregation of schools. Brown II (formally known as Griffin v. School Board of Prince Edward County) came in 1955 after Prince Edward County, Virginia aired grievances asking for more time to implement desegregation.
In the ruling known as Brown II, the Supreme Court ruled that district courts be responsible for ensuring that desegregation occur "with all deliberate speed" (the famed phrase from that ruling). This meant that schools need not desegregate immediately, but must make attempts and efforts to desegregate as quickly as possible.