The times they are a-changing was important in reflecting the fact that a new generation of the young were breaking with the assumptions and the view of life of their parents. The young sought a more truthful, less hypocritical, less selfish way to view the world, and sought ways to try to heal the wounds of society.
Of course not every young person was so inclined, but it was a large groundswell of change, more critical of the world we live in, less inclined to accept things without question. And this happened also around the world. 1968 saw student unrest in many other countries, as well.
Hope this helps, young lady researcher. -- LarryC.