The women were referred to as "flappers" and were seen as rebellious and scandalous. However there is a misconception that all women were doing this at the time, rather it was the middle class of women that had the time and money to dress up as it were. So the changes were limited to a rather small strata of American society and the impact wasn't as big of one as it may seem.
Also note that around this time Jazz was becoming popular (and labelled the devils music) and dancing was changing as well from the waltz and cotillion to faster and more energetic dances. However as noted before it was limited to a small section of society and not all women as a whole.