In the case of Plessy v. Ferguson, what did Homer Plessy refuse to do?

Refused to leave a Whites Only railroad car.

It is important to note that the entire thing was set up as an experiment. Louisiana had a "Separate But Equal," doctrine of law that said blacks and whites could be segregated but that blacks must be provided for equally. This equality very rarely was anything like what we would typically describe as equal, but that was the law.

This meant that train cars could be segregated, and so Plessy was part of a group that wished to challenge this segregation. The whole thing was organized, with the train company knowing he was going to do it. They opposed the law for the obvious reason that it meant they needed to provide more cars. The group hired it's own detective with arresting powers, so that someone else wouldn't arrest him and charge him with a different crime. He sat, was asked to move, refused, and the detective arrested him.

The case is actually Plessy v. State of Louisiana, but the judge's name was Fergusson, so when the case was appealed to the Supreme Court of Louisiana it became Plessy v. Fergusson. Fergusson had convicted Plessy and fined him $25.

The State Supreme Court upheld the conviction citing similar laws in two northern states: Massachusetts and Pennsylvania.

The case was taken to the United State Supreme Court on further appeal and again the conviction was upheld. The case was argued based upon infringement of Plessy's 14th Amendment Right to Equal Protection Under the Law. Equal Protection is the idea that all citizens are guaranteed the same rights. In a 7 to 1 decision, the Court upheld the conviction saying that it did not believe his 14th Amendment Rights had been infringed.

This case is VERY important in US history as it legitimized the Southern policy of Jim Crow laws and set about a whole period of segregation which did not end until Plessy v. Fergusson was overturned by Brown v. Board of Education in 1954 which led to another period of American History known as The Civil Rights Movement.