Surely Plato is the greatest philosopher that ever lived. The questions he asked are still asked today. He was greatly influenced by Socrates and after the death of Socrates in 399 BCE he left Athens and may have visited Egypt, although he certainly visited Sicily. On his return to Athens he established his academy, which may be considered the first university. Apart from "The Apology", which is reputed to be the defence of Socrates at his trial Plato's works are in the form of dialogues, these dialogues are notoriously difficult to date as we only have style to go on. They are divided into three groups, early, middle, and late. In the early dialogues we have what is probably the closest we can get to an individual presentation of Socrates, in the mid to late dialogues Socrates is simply a voice for Plato. The early dialogues show Plato dealing with problems that Socrates himself was most likely himself concerned with, for example, the claim that virtue is knowledge or that all wrong doing is due to igorance, so that no one does wrong on purpose. It seems that Plato himself is simply presenting or raising these problems without any answer of his own. In the middle dialogues Plato's interests broaden and here we have the idea of knowledge and the forms. Socrates had insisted that we must be able to answer the question "what is X" before we can say anything about X. By considering this question Plato seems to have come to the conclusion that there must be some unambiguous example of justice, not in this world but in some other, and that we once must have been acquainted with it. This is what he calls the "Form" of justice. So his theory is we are born into this world with this form, and that is why we have some conception of what justice is, although it is an imperfect one. Which explains why we cannot answer the question posed by Socrates - "What is justice?". It turns out that the Form or Forms are both perfect examples and universal.
In "The Republic", a middle period dialogue Plato sets out his ideal state, which is very authoritarian (Plato was no democrat), he begins from the premise that only those who know what the good is are fit to rule, and he prescribes a long and rigorous period of intellectual training which he thinks will yield this knowledge; & here comes the analogy:
Most of us are prisoners in a cave underground able to see nothing but moving shadows which we take to be the whole of reality, the world outside the cave is in fact the real world of the Ideal Forms, available to the intellect but not to the senses. We escape from the cave by a process of philosophical enlightenment.