How is Plessy vs. Fergusson related to Brown vs. Board of Education of Topeka, Kansas?
These two cases are related in that Brown overturned Plessy.
Plessy was a case that was decided in 1896. In that decision, the Supreme Court ruled that segregation in public accommodations (specifically train cars) did not violate the 14th Amendment's guarantee that all people will have the "equal protection of the law." The court ruled that separate accommodations for the races were legal so long as they were equal.
Brown overturned this rule. In Brown (decided in 1954), the Court ruled that segregation (at least in public schools) was a violation of the 14th Amendment. It ruled that there could really be no such thing as truly equal schools so long as schools were segregated.
By making this ruling, the Court overruled Plessy and helped clear the way for the gains in civil rights in the 1960s.