What was the outcome of the court case Plessy v. Ferguson?

In the case of Plessy v Ferguson (1896) the Supreme Court controversially upheld the constitutionality of racial segregation laws. It was held by the plaintiff and his lawyers that racial segregation under the Jim Crow laws was in violation of the Fourteenth Amendment's equal protection clause, which prohibited states from denying anyone equal protection under the law. The Fourteenth Amendment had been passed during Reconstruction and was designed to outlaw the kind of racial discrimination embedded in the law before and during the Civil War.
In Plessy, the plaintiff argued that the provision of separate accommodation for railroad passengers on racial grounds was in breach of the equal protection clause. The Court, however, disagreed, holding in a 7-to-1 majority that, so long as the relevant facilities were "separate, but equal," then there was nothing unconstitutional about such measures. In reality, of course, railroad accommodation for African Americans was anything but equal.
Yet the Court overlooked the substantive issue of social equality and concentrated instead on the matter of legal equality. As the Fourteenth Amendment was concerned with legal equality, the Court held there was nothing in the provision of separate accommodation for non-whites that violated that equality. If the races wished to remain separate, that was no concern of the Court. This was a social, not a legal issue and, as such, beyond the law's remit. Courts of law should not be in the business of forcing people of different races to mix.
The Supreme Court's ruling in Plessy set back the cause of civil rights for decades. All kinds of facilities in the South remained completely segregated along racial lines—not just trains, but buses, schools, restaurants, bars, beaches, even drinking fountains. It wasn't until over half a century later, in Brown v Board of Education (1954) that the Court overruled its early decision in Plessy and finally dismantled the legal apparatus of segregation.