In the case of Plessy vs Ferguson, the supreme court focused its decision on the interpretation of what word

The word focused on was:

Equal

In context, the overall phrase focused on was the concept of "separate but equal."

Explanation/details:

Homer Plessy is the man behind the famous Supreme Court case, Plessy v. Ferguson. The state of Louisiana had passed a law in 1890, segregating blacks from whites on public transportation. In 1892, Plessy, who was 1/8 black, bought a first class train railroad ticket, took a seat in the whites only section, and then informed the conductor that he was part black. He was removed from the train and jailed. He argued for his civil rights before Judge John Howard Ferguson and was found guilty. His case went all the way to the Supreme Court which at that time upheld the idea of "separate but equal" facilities.

Several decades later, Plessy v. Ferguson was overturned. Brown v. Board of Education of Topeka, decided by the US Supreme Court in 1954, extended civil liberties to all Americans in regard to access to education. Until that decision, it was legal to segregate schools according to race, so that black students could not attend the same schools as white students. The older Supreme Court decision, Plessy v. Ferguson (1896), which had said that separate but equal facilities were okay, was thus challenged and defeated by Brown v. Board of Education. Segregation was shown to create inequality, and the Supreme Court unanimously ruled segregation to be unconstitutional.