It's not just slavery. Slavery was just the worst example of the systematically inferior treatment blacks received in this country. Basically all non-white racial groups were susceptible to it, but it seems to have been stronger the darker the skin of the group. Even within ethnic groups, lighter-skinned folks tend to receive less discrimination than darker-skinned folks.
But I digress. It was slavery, Jim Crow, and all those other legalized systems that denied black access to things in society that we take for granted. And it was not that long ago, either. My parents are in their 50s and they can remember growing up where blacks could not eat at the same restaurants (or had to eat in the kitchen), could not use the same bathrooms, could not attend the same schools, had to sit in the balcony at the movie theater, had to jump through impossible (by design) hoops to get to vote, could not enroll in 99% of colleges in their state and neaby states, and the list goes on. Even in college (in Ruston), my dad was the only white person on his work crew and there were a lot of restaurants and gas stations that they could not all receive service at (or had to get service "around back").
Thankfully these overt, legalized, and systematic forms of oppression have largely been eliminated. But the effects of those are not going to go away overnight--or even in just 30 years. And as for the current inequities, these things build on themselves.
Look at education, for example. The best predictor of academic achievement is the level of education of one's parent. For most of our history, blacks were denied basic education, so, as a group, they missed most of the benefits of the education boom in the late 19th and early 20th centuries. Even in the latter half of the 20th century (1950s and 1960s), it was definitively demonstrated that the schools blacks were permitted to attend were inferior to schools whites attended.
So while whites, on average, were making gains in academic achievement with each successive generation, blacks were basically standing still, as uneducated parents raised their children. As blacks have taken advantage of the educational opportunities now available to them things are slowly starting to improve, but it is going to take time to start to see generational effects.
There is clear evidence that things are better in America than they've ever been with regard to race, but let's not kid ourselves into thinking that everyone is now automatically on equal standing just because our schools are integrated and there is a black man in the White House. Our country continues to bear significant scars from centuries of overt, systematic, and inexcusable racial oppression, and while a lot of healing has taken place, we still have a long way to go.