Plato wrote the Allegory of the Cave to illustrate his belief that our everyday perceptions do not capture ultimate reality. In the allegory, prisoners are chained in a cave and can only see shadows projected on a wall. This represents how people rely on sensory perceptions rather than intellectual understanding. The document discusses themes in the allegory like ignorance and how breaking free of preconceived notions allows one to comprehend true forms rather than imperfect shadows. It also addresses Plato's view that people can choose to free themselves from limited perceptions through questioning and seeking knowledge.