One of Cuba's greatest living historians, Alejandro de la Fuente, wrote an excellent op-ed about race relations in Cuba in the New York Times, found here. As he points out, race relations in Cuba are some of the best in the entire hemisphere, with blacks being more equally represented in jobs/politics (relative to the rest of the population) than almost anywhere else in the Americas. Keep in mind, he writes this while in exile from Cuba, so he could easily write an anti-Cuba diatribe, but he doesn't. That says a lot.

In short, relations improved greatly. Castro's numerous and greatly beneficial social programs affected mostly the poor. A good part of the poor and marginalized population was either black or mixed race, so it benefited a huge portion of black people.

Although having one of the highest literacy rates in Latin America at the time of the Revolution (coming in at 4th with 76% literate), a good quarter of the population was still completely illiterate and many others were functionally illiterate. Cuba eliminated illiteracy almost completely within 10 years.

Cuba created a series of special social projects, like Barrio Especial José Martí in Santiago de Cuba, which tore down the shanty houses many lived in, replacing them with cheap but dignified homes with electricity and running water. These homes had issues, since many were then not taken care of by their residents who quickly ran them into the ground, but it was still a huge step up from huts the poor would often create on the margins of the big cities [I can't seem to find a source online for Barrio Especial José Martí, but it was a part of a special course on art and architecture during the Revolution].

With a free education system, even in higher education, Cuba knocked down one of the principal hurdles of racial inequality. Black people were poor in part because they had no education. They had no education because they were poor. Prejudice has and will still play a part, but it is far less a definitive impediment than simply not having the money. Now black graduates reflect far more closely the total number of blacks in Cuba. With that said, black and mixed race students are still less common than they should be, given their proportion in the general population. The gap is small relative to racial inequality gaps in the rest of the hemisphere (including the US) but it is there. De la Fuente touches on this in his article.

Not only are black contributions emphasized in education, like the fact that slaves made up most of the independence forces, but black writers, poets, etc., have broken from the mold of just being musicians and minstrels. One of Cuba's premier writers right now is Leonardo Padura and the history of the Revolution is filled with black writers and artists, like poet Nancy Morejón.

Black people, as de la Fuente comments, are still disproportionally represented in jails, they are still not adequately represented in higher education, and a strong subcurrent of racism is still very much present in daily life, starting with blacks themselves, but things have certainly gotten better under the Revolution and seem to be on their way to improving even more.

In conclusion, I'd like to note that Cuban concepts on race are also slightly different from American ones. Cuba has a long, long history of racial mixing. The first Spaniards to arrive and become little aristocrats brought few women with them, so their sons and daughters seem to have been mostly mixed with natives. New elites moved in, attempts to whiten the bloodlines of old elites occurred, etc., but that lack of racial 'purity' is a constant in Cuban history. There is even an old saying, 'el que no tiene de Congo tiene de Carabalí' (who who doesn't have [a little] Congo has [a little] Carabalí [in him]). Or another saying, 'yeah, but where's your grandmother?', which is used when someone says they're white, implying that they may look white but if you went back far enough you'd find plenty of non-whites. Racism in Cuba was more perverse, with white as a status that could be attained, instead of an impassable barrier.

I hope that answers your question.

Edit: Free healthcare was another obvious way (mostly poor) black people benefited.