oops, I edited the thing while you were commenting... sorry! :) Yes, Abigail Adams, despite her own protestations to the contrary, was an unusually well-educated woman. It is not surprising at all that she advocated a more "meaty" education for females, but the fact that she was so outspoken, and indeed heeded, is really remarkable.
A basic definition (from sparknotes) is: "Republican motherhood was the concept that women should educate themselves and be educated in the principles of liberty, independence, and democracy so as to inculcate the coming generation with these republican values. This was one sign that women were becoming more respected as intellectually capable."
Also this paraphrasing of Linda Kerber's work (she's the one who coined the phrase) that I found on the web: Republican motherhood came into American ideology after the Revolution. There was much concern over where the new nation was heading and how the republic would develop. In the early republic a consensus developed around the idea that a mother, committed to the service of her family and to the state, might serve a political purpose. Those who opposed women in politics had to meet the proposal that women could- and should- play a political role through raising a patriotic child. The republican mother was to encourage her son's civic interest and participation (Kerber 1980, 283).
The concept that women could be useful to the republic without even being citizens was a new one at the time (1780 to 1830 or so), but this was almost the first time the participation of women in the republic on any level had been portrayed as a positive thing. Republican motherhood had the (from our modern perspective) positive points of making a solid argument for the education of women in politics and government (and by extension in other subjects that women were not "supposed" to be taught, like math, science, or anything but music and novel-reading... c_b says sarcastically), and for valuing women (who were at this time by law considered the property of their fathers or husbands) as contributing to the republic and, indeed, assuring its continued existence. The drawbacks (and there were a few) were that it kept women's intellectual achievements from being acceptable outside the home or even outside their own sons' education.
Actually I was going to start typing this huge long thing and realized, there's probably an article on it somewhere, and there is: Wikipedia.