Plessy v. Ferguson is one of the most famous (or infamous) of American Supreme Court cases. It was decided in 1896 and it made racial segregation legal.
The 14th Amendment to the Constitution says that all people must get the "equal protection of the laws." In Plessy, the Court said that segregation of blacks and whites did not deny blacks that equal protection. It said that so long as blacks were given equal accommodations in things like railroad cars it did not matter if they were kept separate from whites. This was the "separate but equal" doctrine that lasted until the Brown v. Board of Educationdecision in 1954.