Historical Context
Plessy, an African-American sat in a railway car reserved to white persons He was asked to sit in a car for black people, but he refused, saying that it violated the XIII and XIV amendments of the Consitution
Legal issue at stake in the case
May the XII amendment (prohibiting slavery), and the XIV amendment (to secure rights of the former slaves) be taken in consideration in this case?
Question(s) the Court has to answer
Is the public separation between whites and blacks constitutional?
Supreme Court ruling
The separation by railway companies in railway cars for races is not against the XIII amendment (the Court didn't see in what it was concerned), and not against the XIV amendment, because the separation doesn't mean the inferiority of blacks, as the living conditions in the cars are the same.
Dissenters?
One dissenter: Justice Harlan.
"But in view of the Constitution, in the eye of the law, there is in this country no superior, dominant, ruling class of citizens. There is no caste here. Our Constitution is color-blind, and neither knows nor tolerates classes among citizens. In respect of civil rights, all citizens are equal before the law."
(http://www.law.cornell.edu/supct/html/historics/USSC_CR_0163_0537_ZD.html)
Political/Social aftermath and debates
"Plessy legitimized the move towards segregation practices that began earlier in the South. Along with Booker T. Washington's Atlanta Compromise address, delivered the same year, which accepted black social isolation from white society, Plessy provided an impetus for further segregation laws. In the ensuing decades, segregation statutes proliferated, reaching even to the federal government in Washington, D.C., which re-segregated during Woodrow Wilson's administration in the 1910s." (Wikipedia)
This Decision was overruled by a decision of 1954, Brown v. Board of Education.