What is the doctrine of "separate but equal"? • What is the difference between social equality and political/civil equality?

In the case Plessy v. Ferguson, the Supreme Court determined that segregation was allowed as long as the facilities were "separate but equal." This was overruled with Brown v. Board of Education

With Brown, African-Americans were given civil equality but were still treated as second class citizens and were thus not socially equal. So, social equality is how people actually treat each other while political equality is how they are treated by the law.