The idea of separate spheres had to do with male and female roles. The idea of separate spheres held that men and women belonged in separate parts of society. Women were supposed to stay at home and keep out of the public eye as much as possible. Men were supposed to be the ones who had to go out in public to do things like earning a living.
The idea of separate spheres came to be more prevalent in the United States in the early 1800s. The idea became more and more popular as America became more of a market-oriented society with people working away from their homes (as opposed to doing subsistence farming or working in home workshops). When this happened, women came to be identified with the home, which was now outside of the economic sphere. With this change, women came to be seen as incapable of participating in the economic and political world outside the home.