In the Apology, Socrates presents, in defense against his indictors, the reasons why he was considered by the Delphian Apollo to be the wisest man. While it may be logical to think that he was deemed so because he knew more than others, the reson of his wisdom lay precisely in the contrary statement. After examining several classes of professionals reputed skilled, Socrates realized that the defect that deprived them of wisdom was that they thought to be wise because of their skills. This statement was the reason of the hatred against him, which later turned into judicial indictment. Thus, not only did consciousness of wisdom mean rather a lack of wisdom, but also wisdom was now deemed to reside elsewhere than in mere professional skills.

It is Plato who later defined the meaning of education:

At present, when we speak in terms of praises or blame about the bringing up of each person, we call one man educated and another uneducated, although the uneducated may be sometimes very well educated for the calling of a retail trader, or of a captain of a ship, and the like. For we are not speaking of education in this narrower sense, but of that other education in virtue from youth upwards, which makes a man eagerly pursue the ideal perfection of citizenship, and teaches him how rightly to rule and how to obey. This is the only education which, upon our views, deserves the name; that other sort of training, which aims at the acquisition of wealth or bodily strength, or mere cleverness apart from intelligence and justice, is mean and illiberal, and is not worthy to be called education at all.
Laws I: 643-4

The important point in this passage is that Plato here differentiates between education and training. To him, education was of the utmost importance in the upbringing of the citizen within the phratry of the polis, the city organized after the divine pattern which we ought to contemplate. He clearly explains that education, the one that deserves the name, aims first and foremost at the perfection of the soul. Because the soul is the only reality, it is her that we must polish and cultivate first of all. Education, in this sense, was to make the citizen of the polis as perfect as he ought to be in order to conduct the affairs of the city as justly and rightly as possible, so that it may ressemble as closly as possible the divine prototype, God. In the Republic, Plato develops an entire allegory of the human soul with the city: both achieve excellence only so far as they are patterned after the divine prototype. He who rules himself is also able to rule the city, because he conforms to the model of the supreme good. All of Plato’s ideas on education–what ought to be allowed or not, the manner in which it is to be taught, etc–are thus based upon this principle: its chief aim is the improvement of the soul, and whatever threatens to dirt it is to be discarded, so that it may as the result of this beautification attain to divine status, and its tangible result is the fraternity and perfection of the polis.