What did Plato mean when he said that the state is man writ large and what did this have to do with his view of the human psyche?

Plato meant that the structure of an ideal state, with its three classes (rulers, guardians, and producers), reflects the three parts of the human soul (reason, spirit, and desire). Just as a state functions best when each class plays its proper role, an individual's soul achieves harmony when reason rules over spirit and desire. Plato believed that both the state and the individual soul should strive for this ideal balance to achieve justice and Excellence.