Radical reconstruction was a way to help bring the south back into the union. Most Southern states had to create a new constitution and the south was divided into military districts. There were five military districts. It was not very effective.
However, race relations would get worse before they got better. There is the Plessy decision that said separate but equal is okay. Separate but equal was truly unequal. The 20th century Civil Rights Movement shifted the way the country would view race relations. During this time you have the Brown v. Board of Education that shot down the Plessy decision. Dr. Martin Luther King, Jr and his movement fought to register southern blacks to vote. Mass media played a key in showing the American people how blacks were treated in the south.
Although Reconstruction failed to do much to advance racial equality in its own time, it did lay the foundation for future racial equality in that it allowed the passage and ratification of the 14th and 15th Amendments to the US Constitution. These amendments are the basis of legal racial equality today.
The 14th Amendment guarantees that states cannot deny the equal protection of the laws to anyone. This eventually was taken to mean that they could not enact laws or policies that would segregate the races or otherwise treat people of different races differently. This is a major source of legal racial equality, having been used, among other things, in the Brown v. Board of Education decision.
The 15th Amendment guarantees that people will not be denied the right to vote on the basis of race. This has helped gain greater racial equality for African Americans (though we in the US, of course, do not have complete racial equality yet) by eventually allowing them a voice in the political process. Since African Americans have the vote, politicians have to pay at least some attention to their needs.
Both of these amendments were only ratified because of Radical Reconstruction. The state legislatures in the South would surely not have voted to ratify. Partly because of this recalcitrance, the Congress imposed Radical Reconstruction and essentially forced the states to ratify these amendments as a condition of regaining their right to self-government. In this way, Radical Reconstruction laid the foundations for or planted the seeds of the degree of racial equality that has been gained in the last six decades or so.