The rational part (logistikon) is the seat of reason, knowledge, and the love of truth. The spirited part (thymoeides) is the source of anger, honour, and indignation — it bristles at injustice and craves distinction. The appetitive part (epithymetikon) is the source of bodily hungers: food, drink, sex, and money.
Each part has its characteristic virtue when it performs its proper function. Reason's virtue is wisdom. Spirit's virtue is courage. Appetite's virtue is temperance — not the absence of desire but its willingness to be governed. Justice in the soul is the harmony of all three: reason ruling, spirit supporting it, appetite accepting its authority.
The tripartite soul is not merely a psychological theory — it is the key to Plato's political philosophy. Every type of city corresponds to a type of soul: the philosophical city to reason's rule, the democratic city to appetite's rule, the tyrannical city to enslavement by a single monstrous desire. To understand a constitution, look at the psychology it cultivates.
Plato's tripartite soul in The Republic (Book IV) influenced Freud's model of id, ego, and superego — though Freud's divisions track differently.