How does women’s access to education/literacy affect their rights in their countries?

Research has supported the connection between education for women and the attainment of women's rights and gender equality in their respective countries. For example, an additional year of schooling for a woman has been shown to result in a 10–20% increase in her wages. This increase helps decrease economic inequality and promotes gender equality across the society. 
In addition, women's education is connected to lower infant mortality, lower numbers of average children per woman, and lower maternal death rates. Women with smaller families tend to live better in many countries. In addition, women who have greater education are generally better able to make sound choices about the healthcare of themselves and their children; they can read and reason more effectively in many ways. Women with better health are better able to advocate for themselves and their children. 
In addition, women with higher rates of education can participate more fully in the political life of their countries and advocate for their rights. With education they can understand the issues being discussed, can contribute to the discussion because they are literate and well informed, and can participate in political movements that will further their rights and power. Moreover, because educated women can read they are able to understand how others in their country, and in other nations, have achieved rights and can work toward achieving those selfsame rights for themselves.
Women with more education are also often able to exercise greater power in the  decision-making of their families. They can more effectively advocate for the education of their daughters—thus furthering women's rights for the next generation—and help their daughters make decisions about their lives that will result in greater gender equality (such as delaying the age of marriage).
Sources:
Klasen, Stephan. "Low Schooling for Girls, Slower Growth for All? Cross-Country Evidence on the Effect of Gender Inequality in Education on Economic Development." The World Bank Economic Review 16, No. 3 (2002): 345-373.
Levine, Ruth, Cynthia Lloyd, Margaret Greene, and Caren Grown. Girls Count: A Global Investment and Action Agenda. Washington, DC: Center for Global Development, 2008.