Republican motherhood was a concept that mothers were the moral guardians and protectors of the New Republic. Mothers also needed to raise civic minded sons and in order to do that, women needed to be educated. Republican motherhood was important because it added a civic dimension in their sphere (which also means it broadened their sphere from just domesticity). Moreover, it allowed women to be educated. This allowed women today their right to education so be proud of these Republican mothers who fought for women's education today. Without them, education would probably be impossible for women because men from then were the only ones granted the right to education.
Just some food for thought...