1) Plessy vs. Ferguson was an 1896 Supreme Court case in which the Supreme Court ruled that "separate but equal" facilities for whites and blacks were legal. The justices ruled that this idea of "separate but equal" DID NOT violate the 14th amendment of the US Constitution.
2) Brown vs. Board of Education was the Supreme Court case that overturned Plessy vs. Ferguson. This 1954 case saw the Supreme Court justices rule that separate but equal was indeed a violation of citizens constitutional rights. In Brown vs. Board of Education II, the Supreme Court ordered that all schools must integrate "with all deliberate speed."