In order for a democratic society to even function as intended to, there must be public education. Democracy is a system of government by the people. People are, in theory, the supreme power. They exercise their powers though voting, freedom of speech, practicing liberty and equality, etc. However none of that means anything without education. What is the point of having the ability to vote and make decisions, if the voters don't fully understand democracy? How are they supposed to make thoughtful, and informed decisions for issues on which they have never been educated? They cannot and that is why it is the government's responsibility to educate the generations that will one day be in charge.
Every student learns all about democracy in school. Most importantly, they learn about the challenges it faced in the past. This gives insight on how to handle issues in the future. For example, during a large part of history, African Americans and women had limited or no rights. Over time that changed. People realized their wrongdoings and worked to fix it. Hundreds of years later this is still relevant. Today, you could use the same arguments to fight for gay marriage equality or for women's ongoing fight for equal pay. Democracy can always be expanded and improved upon. Education makes that possible.
Furthermore, education also instills democratic ideals. As early as kindergarten, children begin reciting the Pledge of Allegiance, which refers to the characteristics of a democracy—liberty and justice. As students get older, they begin to consciously practice the democratic ideals. For example, many school students hold election and vote for their peers to enter office. This is democracy in action, granted it is a baby step, but it still counts.
In one history class I've taken, we held a different debate every week on some of the country's most important and frequently debated issues. Not only did these debates teach students about new subjects, but it also allowed them to learn and make informed opinions. Students then went on to debate their side, practicing freedom of speech and individuality in the process. Activities like this are preparing students during their education to be able to handle the adult world, as being part of a democracy is not just a right but a responsibility. It is after all, a government of the people. In order for a democracy to work, the people must be educated. Essentially, education is the base of democracy.