The Plessy v. Ferguson case was important because it established the constitutionality of "separate but equal" laws, in which states segregated public services and accommodations for African-Americans and whites. Decided in 1896, Plessy v. Ferguson dictated racial law throughout the country until Brown v. Board of Education in 1954, according to PBS.
In 1892, Homer Plessy, a 30 year old man of mixed ancestry, took a seat in a segregated train car for whites only in Louisiana. When asked for his identity, he identified himself as black and was subsequently arrested. Plessy appealed his conviction all the way to the Supreme Court, arguing that the Louisiana state law violated the 13th and 14th Amendments. In the end, the Supreme Court voted 7-1 to uphold Louisiana's segregation laws, paving the way for more segregationist laws throughout the American South. The decision technically only validated these laws as long as the accommodations provided were "separate but equal" in quality, and while some states occasionally attempted to meet that expectation, the reality of the situation was that most services provided to African-Americans were woefully inadequate compared to those offered to whites. In 1954, Brown v. Board of Education established that separate facilities were inherently unequal under the law, and overturned Plessy.