He sees himself as a seeker. Human wisdom vs. divine wisdom. God knows what is best. Socrates' friend Chaerephon consulted the oracle at Delphi. According to the oracle at Delphi, no man was wiser than Socrates.
Self understanding means self-improvement.
One must transform one's own character in the light of one's vision of what is best. True knowledge or human wisdom is not abstract information or facts that fill the brain. It is knowledge that transforms character, brings order to a disorderly life, refines attitude, makes one better. Socrates examined the unexamined lives of others. He cross-examined the politicians, those whose concern was supposed to be the common good.