There were so many important events in the '60s that it is hard to pick just one. I will pick the introduction of oral contraceptives as the most important event of the '60s.
The coming of "The Pill" was hugely important because it contributed to two fundamental changes in our society. First, it contributed to changing sexual morality. By making it relatively easy for women to engage in sex without becoming pregnant, it helped to erode the expectation that sex would take place only within marriage. Second, it contributed to changing relations between the sexes. As women became more able to control when/if they would get pregnant, more women came to be able to work outside the home. This changed expectations about the role of women both in society and within their marriages.
The Pill, then, had a tremendous impact on our society, changing some fundamental moral beliefs as well as the nature of relations between men and women.