The importance of the music in the 60's
Music of the 1960's served as the voice of that generation.
Music of the 1960's was characteristic of the revolution that was going on during the decade. It was a time of rebellion and counter-culture in which the younger people were questioning everything, including authority, corporations, the government, and other aspects of everyday life. It was essentially a revolution of the status quo. This gave rise to the Civil Rights Movement of the decade along with other movements that affected the rights of society as a whole.
Going back to the 1950's, transistor radios and car radios made a big difference in how much music teenagers heard or where. Kids could listen to the radio, records, or go to places with jukeboxes or even live music almost any time.
In the early 60's, folk music, with singers like Peter, Paul and Mary, and songs written by Bob Dylan and others started talking about themes like war, and racial injustice, things that had rarely been in popular music (but folk music) before. As the war in Vietnam heated up, there was more music against the war, against injustice, for brotherhood.
Just the fact the Beatles had long hair caused huge problems between parents and guys who wanted to grow their hair long. Of course as the sexual revolution and drug culture spread, the songs reflected that, although often in terms than were ambiguous. Often parents would tell kids not to listen to certain songs because they might be about drugs if the parents couldn't figure out the lyrics. The hippie movement, Woodstock, etc. reflected the changes in attitudes in the teen and young adult culture and that in turn was reflected in the music.
Music was somewhat of a factor in the Civil Rights movement. From 1957 until some time in the early to mid 1960's, the music-dance show, "American Bandstand" was on every afternoon.
Often they had live entertainers. Sometimes they were African American, at a time when Blacks were almost never seen on TV, otherwise. It has been said that in some small part, seeing Chuck Berry or Sam Cooke or the Drifters on American Bandstand influenced kids in a subtle way that Blacks were not all bad and their music, and especially the music of Motown in the 1960's had an influence on how some White kids thought of African Americans.