This is a very simple question which often comes with complex answers. Briefly, classical education is the traditional model of education which employs the liberal arts and the great books to form young minds in truth, goodness and beauty so that students may live a virtuous life and grow in wisdom and eloquence.
Classical education focuses on the studies of grammar, logic, and rhetoric in order to form students to be experts in the arts of language. It teaches students to be lovers of learning, to seek the truth, and to appreciate literature, history, poetry, music, etc.
Classical education is multifaceted in its pedagogy (how it teaches) and curricula (what it teaches). In short, classical education teaches the best things in the best way for children to learn effectively and permanently.
What we believe about the nature of the human person will affect how we educate our children and what we decide to teach them. If a man is merely flesh and blood, and there is nothing supernatural about him, then what matters is only this earthly life and living comfortably. As educators in this scenario, we would focus on teaching the child how to perform tasks in order to succeed in a job, or to achieve other pragmatic ends. This is largely the aim of most American schools today since they have mostly adopted this modern, progressive view of education based on their metaphysical and anthropological assumptions about the human person.
If, instead, we view man as made in the image and likeness of God, that he has an eternal soul with an intellect and will, then we would see that these must be properly formed in order that he may make good moral decisions both for the good of himself and for the community at large. Consequently in the world of education, we would aim to inculcate virtue in this student, and teach him how to live and learn rightly, in accordance with the Truth.
In the Catholic perspective, the truth is not merely the correspondence of something to reality, the truth is actually a person, Jesus Christ, who said, “I am the way, the truth, and the life.” We conform our minds and hearts to those of Christ, so that we may know and love what is good, true, and beautiful. This is the path to authentic human happiness and our destiny to which our Lord has called us: unity with Him in heaven.