The lives of young people changed dramatically during this decade in the sense that they got more and more freedom during those years.
At the beginning of the '60s, the US was still a very straightlaced place. For example, my mother entered college in 1961 and was not allowed to wear pants on the campus of her public university. This was a time when young people's lives were still quite controlled in ways like that. By the end of the 1960s, the idea that young people's lives would be so circumscribed had completely disappeared. This was due in large part to the push by people like the Hippies. It was also seen in the growth of the youth culture in which young people listened to rock and roll music and generally enjoyed much more freedom than they previously had.
During the 1960s, young people in the US gained much more of an ability to live their lives (for good or for ill) much more in the ways that they wanted to, as opposed to living in the ways that society and authority figures thought that they should.