First and foremost, the "new woman" was one who had shed the old ways that said that women should stay at home and be invisible or (when out in public) be very demure. Instead of staying at home all the time, many of the new women worked outside the home. These were not always good jobs, but they did put women out in public. While out in public, women did not act demurely as the old ways demanded. Instead, they dressed and acted in new and more "forward" ways. They wore shorter skirts and lighter clothing. They wore more makeup and they were willing to smoke in public. All of these things would have been unthinkable in the past.
In short, the new woman was a more aggressive and outgoing person than women had been in previous generations.