There are many answers to that question. Here are my key elements of a classic education:
1. It teaches children according to the trivium. During the first four years of a child's schooling (approximately 1st through 4th grade), children love to learn and memorize. This is called the grammar stage. They are little sponges. It comes easy for them. So, we fill that sponge up. During these years we immerse the child in stories, facts, and ideas. They also do a lot of memorizing during this time. They may not understand everything they learn but we pound the pegs in so that later when we dig deeper, they are familiar with the ideas. The second four years of schooling (5th through 8th grade), we teach the child how to think. This is referred to as the logic or dialectic stage. This is when they really start asking why and want a decent answer to that question. We teach them logic. They learn how to work through ideas, finding the fallacy and truth in them. The third stage of learning (9th through 12th grade) is the rhetoric stage. During this time they learn how to express ideas. They gathered the information during the grammar stage, thought about the information during the logic stage, and now speak and write about what they think about these ideas during the rhetoric stage. The trivium is sometimes compared to a computer: input (grammar), process (logic), and output (rhetoric). This is how children naturally develop, and we teach them in accordance with these abilities.
2. It is systematic. Classical education works through history chronologically, integrating science, literature, and art developments during these same time periods. Every four years, corresponding with the trivium, we will cover all of world history from creation to modern time.
3. It embraces the great books. During high school, our children will be reading unabridged original books, not textbooks or watered down versions. This can occur because they have been exposed to these ideas before. This last year we studied ancient times. We read a child's picture book version of "The Odyssey." In four years, we will again study the ancients. This time we will read a more difficult version of "The Odyssey." By the time we reach high school and read the original "The Odyssey," it will not be too intimidating because we are already familiar with the story.
4. It teaches Latin. Yes, I know that no one speaks Latin anymore. However, Latin is the base for many modern languages. If you know Latin it will be much easier to learn other languages. The process of learning language is a good exercise for the mind and forces you to understand the grammar of English. Latin also gives you a head start in other areas where Latin word roots are used such as science and law.
Disclaimer: I did not learn this way so I am relatively new to these ideas and in no way an expert. There are many different thoughts about what constitutes a classical education. This is just how I hope it looks at our house.