Theodore Roszak created the word "counterculture" to define the rebellions of the youth in the late 1960s. It was then made a movement. Counterculture actually means when the ideology of the people do not match with that of the mainstream culture. They have different values and they try to protest and change them. Examples of a counterculture would be the hippie movement of U.S. in 1960s, the polygamists or the feminists groups.
Counterculture is different from subculture which is a small cultural group within a large one.
