I would argue that the first answer misses out on a number of important historical developments that allowed this to happen, particularly those in between 1865 (as in your tag) and WWII.
First, the rise of big business brought a number of new opportunities for women. The increasing size of businesses led to a demand for women to work (relatively menial) white collar jobs. These included new jobs like typist and telephone operator. Firms liked to have women do these jobs, in part because they worked for lower pay than men might have.
Second, in the first couple decades of the 1900s, there were technological advances that made it easier for women to find the time to take jobs. These were labor-saving devices like washing machines that allowed women to do housework more easily. Because women no longer had to devote as much time to housework, they could have time to take jobs. If women did not want to take jobs, they could also use that extra time to do other things outside the home like going for drives in cars or watching movies (more historical developments).
Finally, it seems that your question does not necessarily refer to women working. Instead, it refers to women doing things other than simply staying in and taking care of the home. A development that encouraged them to get out of the home (without taking paid work) was the Progressive Era. The Progressive Era encouraged women to become more involved in reform work such as settlement houses. This provided another option for women other than staying tied to housework.
This is a great question to consider, and there are a number of different answers that could be given. I suppose one of the key responses is the way in which gradually the opportunities afforded to women changed as time went on thanks to the Industrialisation of society and the way that more jobs were being created that gave women an opportunity to work and earn an income. This gave them a different opportunity from just getting married and being provided for by their husband.
This of course was particularly true during the Second World War, when many women worked in jobs that were traditionally thought to be the domain of men to help the war effort. We can see the way in which this empowered women and gave them an opportunity to contribute to the war, which was originally seen to be a male activity alone. Gradually, through events such as the Second World War, gender was a concept that changed in terms of how women were perceived and the opportunities that they had.