Free will in antiquity
In Plato's Gorgias (and in the Protagoras 345c4-e6), Socrates argues that no one does wrong willingly, one of the most famous doctrines to be associated with him. When framed in modern (Western) terms, the implication is that it is ignorance, rather that free individual agency, that is responsible for morally wrong actions.
Eudaimonia
It emerges a bit further on that this concern for one's soul, that one's soul might be in the best possible state, amounts to acquiring moral virtue. So Socrates' point that the Athenians should care for their souls means that they should care for their virtue, rather than pursuing honour or riches. Virtues are states of the soul. When a soul has been properly cared for and perfected it possesses the virtues. Moreover, according to Socrates, this state of the soul, moral virtue, is the most important good. The health of the soul is incomparably more important for eudaimonia than (e.g.) wealth and political power. Someone with a virtuous soul is better off than someone who is wealthy and honoured but whose soul is corrupted by unjust actions. This view is confirmed in the "Crito", where Socrates gets Crito to agree that the perfection of the soul, virtue, is the most important good: