Given what the character says in the Apology, it seems that Socrates called his practice the "love of wisdom" (φιλοσοφία) and called himself a "lover of wisdom" (φιλόσοφος). The adjective φιλόσοφος can be used generally for someone who has an unusually strong interest in certain intellectual matters, but Socrates seems to have something more specific in mind. He is interested in the wisdom necessary and sufficient for living a good life and being "happy" (εὐδαίμων), and he thinks that the method he uses is the only way for a human being to acquire this wisdom.

(The adjective εὐδαίμων means "happy, blessed with good fortune." The opposite is κακοδαίμων, "ill-fated, ill-starred, miserable.")

(In the subsequent tradition, there was disagreement about whether the wisdom the lover of wisdom pursues is sufficient for living a good life. In late antiquity, there also was disagreement about whether the method the lover of wisdom uses is the only way for a human being to acquire the wisdom involved in living a good life.)

As a lover of wisdom, Socrates is interested in "wisdom and truth and the best state of [the] soul (ψυχή)." This way of talking about wisdom as a state of the "soul" (ψυχή) was part of a way of understanding of human beings. The word ψυχή transliterates as psychē and is a root of the word 'psychology,' and although now it is commonplace to explain why human beings do what they do in terms of their beliefs, desires, and other psychological states, this explanation is not taken to imply that there is a ψυχή that is in these states.

Socrates talks about the Soul

The Clouds of Aristophanes shows that Socrates talked about wisdom as a state of the soul as early as 423 BCE, when Socrates was in his middle forties and Plato was a boy. In the play, Aristophanes uses Strepsiades to make fun of Socrates. He has Strepsiades refer to the denizens of the think-tank that Socrates heads as "ψυχῶν σοφῶν" ("wise souls") who "in speaking of the heavens persuade people that it is an oven, and that it encompasses us, and that we are the embers" and who "teach, if one gives them money, to conquer in speaking, right or wrong" (94-99).

(Aristophanes (446-386 BCE) was an Athenian comic playwright. His Clouds is a brilliant caricature of the historical Socrates and of the new education in 5th century Athens. Anaxagoras introduced the inquiry into nature to Athens. It quickly became an object of suspicion, and Socrates was caught up in the reaction. (Pericles invited Anaxagoras to Athens to become part of his entourage.))

(In the Clouds, when Pheidippides asks who dwells in the "think-tank," Strepsiades replies that he does "not know the name accurately" and that they are "those who are anxious with respect to thinking (μεριμνοφροντισταὶ = μεριμνάω + φροντιστής)...." (101). This language suggests that φιλόσοφος was not yet the common way to describe Socrates.)

(How the ancient Greeks understood the "soul" (ψυχή) changed significantly over time. In the opening lines of Homer's Iliad, the wrath of Achilles is said to send the souls of heroes to Hades but to leave them, the heroes themselves, as food for birds and dogs on the battlefield. (Similarly, in Homer's Odyssey 11.74, the ψυχή of an unburied hero asks Odysseus to bury "him," where "him" refers to his corpse.) Achilles does not think that the souls he sends to Hades are the people he kills. Nor does he think that the soul is something one could improve or make worse, especially in terms of the "love of wisdom," as Socrates supposed. The soul was thought to be necessary for life. A human being dies when the soul departs from his body, but thinking and feeling in the living is not a matter of this soul. Feeling was thought to somehow depend on the blood around the heart. Homer's "souls" are shades or shadows. They are portrayed as witless and feeble images of the living. This is not to deny that the Greeks in Homer's time thought of human beings and their actions in terms of what we would now call "psychological" states and processes. They did, but they did not think of these states and processes in terms of the "soul" (ψυχή). Just how the word ψυχή came to be used this way is not clear. It seems that over time as it became possible to think of human beings after death as being more than witless shades, it became natural to use ψυχή to refer to this way of existing after death and to think that this ψυχή explains thinking and feeling in the bodies of the living.)

Action is a Function of the Soul

Socrates seems to have thought that human beings do what they do in terms of their "soul" (ψυχή) and the soul needs care for one's life to be good.

• human action is a matter of the states and processes in the "soul" (ψυχή)

As "psychological" beings, human beings do what they do because of the states and processes in their souls. If the soul lacks wisdom and thus is in a bad state, the individual makes poor choices in life. If, on the other hand, the soul has wisdom and thus is in a good state, the individual chooses in such a way that his life is good and he is "happy" (εὐδαίμων).

"[H]istorically the decisive step was taken by Socrates in conceiving of human beings as being run by a mind or reason. And the evidence strongly suggests that Socrates did not take a notion of reason which had been there all along and assume, more or less plausibly, that reason as thus conceived, or as somewhat differently conceived, could fulfill the role he envisaged for it, but that he postulated an entity whose precise nature and function was then a matter of considerable philosophical debate.... [W]hat Socrates actually did was take a substantial notion of the soul and then try to understand the soul thus substantially conceived of as a mind or reason. ... By 'a substantial notion of the soul' I [mean]... a notion according to which the soul accounts not only for a human being's being alive, but for its doing whatever it does.... This was not a common conception, it seems, even in Socrates' time, but it was widespread and familiar enough under the influence of nontraditional religious beliefs, reflected, for instance, in Pythagoreanism. And it seems to have been such a substantial notion of the soul which Socrates took and interpreted as consisting in a mind or reason." (Michael Frede, "Introduction" in Rationality in Greek Thought, 19.)

The Soul Consists in Reason

Given that he thinks of wisdom as a state of the "soul" (ψυχή), and given the way he seems to try to instill wisdom by forcing his interlocutors to contradict themselves, Socrates seems to think that the soul consists in reason and that reason is more than the ability to make inferences. He seems to think that reason includes the knowledge that constitutes wisdom. He seems to think that everyone has this knowledge but that everyone is also confused because they have false beliefs. These false beliefs are the problem, and Socrates thinks that eliminating inconsistency in what one believes is the remedy. In this way, as Plato portrays him, Socrates thinks that inconsistency in belief is a kind sickness in the "soul" (ψυχή) that stands in the way of the good life.

This shows why Socrates thinks he is doing something so important in questioning his fellows in the marketplace and elsewhere. He helps them improve their souls by helping them eliminate their false beliefs. In the absence of these beliefs, they would live good lives and be "happy" (εὐδαίμων) because they would live in terms of the knowledge that belongs to reason.

Perseus Digital Library:

Aristophanes, Clouds

Strepsiades is burdened with debt because of his aristocratic wife and the expensive tastes she encourages in their son, Pheidippides.
To solve his problems, Strepsiades tries to enroll his son in the "think-tank" to learn how to make the weaker argument appear stronger.
Strepsiades hopes to relieve himself from his debts by having Strepsiades the family's creditors in court.

Do you see this little door and little house?
I see it. What then, pray, is this, father?
This is a think-tank (φροντιστήριον) of wise souls (ψυχῶν σοφῶν). There dwell men who in speaking of the heavens persuade people that it is an oven,
and that it encompasses us, and that we are the embers. These men teach, if one give them money, to conquer in speaking, right or wrong.
Who are they?
I do not know the name accurately. They are those who are anxious with respect to thinking (μεριμνοφροντισταὶ), noble and excellent.
Bah! They are rogues; I know them. You mean the quacks, the pale-faced wretches, the bare-footed fellows, of whose numbers are the miserable Socrates and Chaerephon.

Henry George Liddell, Robert Scott, A Greek-English Lexicon:

εὐδαιμονία, eudaimonia, "happiness,"
εὐδαίμων, (εὐ +‎ δαίμων), eudaimōn, adjective, "happy,"
κακοδαίμων, (κᾰκός +‎ δαίμων), adjective, kakodaimōn, "unhappiness"
μεριμνοφροντιστής (μεριμνάω + φροντιστής), merimnophrontistēs, noun, "one who is anxious with respect to thinking,"
φροντιστήριον, phrontistērion, noun, "place for meditation, thinking-shop"