In the 19 century
(and before) it was a foregone conclusion that girls were not schooled. For what need did they have of skills other than cooking, cleaning, and sewing? This was true for jews of that time, only to a larger extent, and for the following reason.
Orthodox Judaism discourages its followers from mingling with people of other faiths, for the simple reason that too much exposure to external influences and foreign thought could lead innocent or confused people astray. Sheltered? Yes. Closeminded? Perhaps.
IT didn't necessarily make that much of a difference, as Jews were often banned admission to gymnasiums, universities and the like. Hence, the isolation was enforced almost as much by external means as internal.
Around the turn of the century, however, things started to change in Europe. Admittance to secular establishments was not as unheard of as before, and the 'ism's (Socialism, Communism, etc) were on the rise. People started to rebel, go out more. Religous youth were discarding traditional garb and cutting their hair, reading secular literature and the like.
This sort of thing was more of a problem for the girls than boys - boys went to a yeshiva or cheder from when they were young, and if they didn't quite know everything, they had some sort of concept of what they were discarding, or else they had some beliefs and culture to hold onto. The girls, being 'home-schooled' had no such thing.
Until then, it had been enough for them to absorb whatever they did about Jewish law, outlook, and philosophy from the household. Now, though, with more external influences than before, and more ways to get out and places to learn about foreign and exciting new things, a need arose for some sort of formal schooling.
The accepted place for a woman was at home, and it was expected that girls would be at their mothers' elbows, learning to sew and cook and clean. This wasn't unique to jewish culture.
Schenirer was not Sara's surname, rather it is Yiddish/German for seamstress. She sensed the trend and took note, not the first to be concerned but the first to come up with some sort of solution. While taking refuge in Vienna during WWI she hatched the idea of opening a school, and tried to put it into effect when she went back to Cracow.
Sara was met with tremendous oposition at first, her idea was outrageous and seemed blasphemous. Teach girls how to read, how to write? Let them learn from the holy book? With the backing of one or two rabbis and a mere 6 students, she opened her first classroom.
Sara taught little of the actual written Torah and scriptures, she focused more on ideas and beliefs, aiming to transmit the warmth she felt for her religion to the kids. The reason for making blessings over food. Why modest dress was important. By the end of the year, her students had grown in number to eighty.
By 1924, the school extended to open up a Teacher's Seminary, in which 18 year old graduates were trained to open their own branches of the school in other locations, thus perpetuating Sara's vision.
Sara called her school Bais Yaakov, (House of Jacob) based on a scripture which refers to the women of Israel as such. Today, there are many jewish schools for girls, and thus many different names. Still, in essence they are pretty much the same, varying in curriculum and stringency of observance from one sect/neighborhood to another.
Golly, this whole thing is pretty much from memory. You can tell me dad's a historian...