Socrates' Care of the Soul is explained in Plato's dialogue: Socrates' Defense or the Apology (it goes by both names).

It starts with Socrates being told by the Oracle at Delphi that there is no man wiser than Socrates

Socrates is puzzled by this, because, as he readily admits, he knows that he knows nothing about life.

So Socrates goes around to all the wise men, politicians, Sophists, poets, musicians, laborers, artisans, whoever he runs into basically, and questions them as to how to live life. Upon questioning them he learns that even though they think they know what they are talking about, or profess to be wise in the ways of living one's life with arete (loosely translated from greek as: skill), they know nothing. The only thing they don't know that Socrates knows, is that no one really knows anything concrete about how to live their life. And that's why there is no man wiser than Socrates.

So Socrates' Care of the soul develops as follows:

The first step is the simple belief that there is some kind of meaning or pattern or order behind life. If life is simply a series of absurd events, then there really is no point to ever doing anything, so you should kill yourself to prevent yourself from doing things anymore. You must first admit that it is plausible that there is an absolute in life, there is some meaning, although we may not know what it is, or even be capable of understanding it. This exemplifies a Pious outlook on life, because it shows that you have faith in the mystery of life (one might go so far as to call it "the divine").

The Admission of Ignorance is the next step. To say, "I am a mortal, and limited, and thus I cannot know the absolutes of truth behind our life" is essential. If you believe that you know things, when in fact you don't, that will only distort your thoughts and frustrate your search for the meaning behind life, and how to live your life. This exemplifies Wisdom.

The third step is Questioning. You are unable to know the true meaning of life in its essence. But Socrates believes that you are able to know things about it, even though you can't know it's whole. So you must question life to become a better person. This exemplifies Courage (to forge ahead in the face of the knowledge that you may not get an answer, and even if you do get an answer, you may not like it).

The final step is to have Hope that there exists an answer, and that the divine is not indifferent to the souls of mankind. To treat everything with equal scrutiny under questioning, fueled by this hope for an answer, exemplifies Justice.

Socrates' Care of the Soul is comprised of these four elements then: Belief in Meaning, Admission of Ignorance, Questioning of Life, Hope in an Answer.

This is Socrates' answer to the Fundamental Religious Question of man's relation to the divine. Care of the Soul produces a life that is based around one's soul (identity) and not the material world.

The qualities that these four elements produce in a human are what Plato considers arete (i.e. skill in living). Arete then is: Piety, Wisdom, Courage, and Justice.