What was the importance of the U.S. Supreme Court case, Plessy v. Ferguson, as noted in the nonfiction book, The Warmth of Other Suns?

U.S. Supreme Court heard the case of Plessy v. Ferguson. The case involved Homer A. Plessy, a black man from Louisiana, who sued the state for its new law that prohibited a train passenger from entering a “compartment to which by race he does not belong.” In June 1894, Plessy challenged the law by buying a passenger ticket, sitting in the white area and refusing to move. He was arrested for violation of the state law. The Supreme Court found in favor of the South and established that “equal but separate” accommodations were constitutional.