The 1960s were the time of the Civil Rights Movement. This movement changed the lives of African Americans forever because it led to them getting (in a real way as opposed to simply on paper) the right to vote and the right to be treated equally by the law.
Before the 1960s, it was legal to discriminate against black people in things like employment or inadmission to public establishments. Various tactics used by Southern whites to deny blacks the vote were also legal. Blacks were, quite literally, second class citizens. The 1960s changed all that. The Civil Rights Movement of that decade resulted in the Civil Rights Act of 1964 and the Voting Rights Act of 1965. These laws ensured that blacks truly would be treated as equal to whites in the eyes of the law.