I will leave it to social historians of the 1950s and 1960s to provide a social/cultural context for why this caught fire. At the same time, it is important to point out an important underpinning namely, the work of John Avery Lomax (1867-1948) and of his son, Alan Lomax (1915–2002) both of whom contributed a great deal by way of collection hundreds if not thousands of folksongs. They followed in the European tradition of folksong collecting, virtually creating the field in the US. While many singers adopted the folk sound while writing their own material, the urban appetite for (and much of their material) grew out of the work Lomax, father and son, who not only collected, but made many of their discoveries popular.

The sources are from the dreaded wiki, but the articles are good and provide an adequate overview. See also the Library of Congress article.