This miniseries had a huge impact on popular culture. It was watched by a huge proportion of the country and had an impact on people of all ethnicities.
For many whites, the miniseries was a thought-provoker. It marked the first time that many had had occasion to think about slavery from the black point of view. It helped to bring issues of race and slavery into the national consciousness.
For African-Americans, a major impact was an increase in racial pride. The bravery and resilience shown by the characters in the face of slavery helped to increase the sense of racial pride that had been growing since the 1960s.
On a more trivial note, the miniseries had a huge impact on television for at least a few years. It was the first miniseries to be run on consecutive nights. It gave rise to a number of later miniseries based on books about history. These were series such as those based on Shogunor on The Winds of Warand the other Herman Wouk books about WWII.
In these ways, this miniseries had a great impact on American culture.