1. Plato realizes that the general run of humankind can think, and speak, etc., without (so far as they acknowledge) any awareness of his realm of Forms.
2. The allegory of the cave is supposed to explain this.
3. In the allegory, Plato likens people untutored in the Theory of Forms to prisoners chained in a cave, unable to turn their heads. All they can see is the wall of the cave. Behind them burns a fire. Between the fire and the prisoners there is a parapet, along which puppeteers can walk. The puppeteers, who are behind the prisoners, hold up puppets that cast shadows on the wall of the cave. The prisoners are unable to see these puppets, the real objects, that pass behind them. What the prisoners see and hear are shadows and echoes cast by objects that they do not see. Here is an illustration of Plato's Cave:
4. Such prisoners would mistake appearance for reality. They would think the things they see on the wall (the shadows) were real; they would know nothing of the real causes of the shadows.
5. So when the prisoners talk, what are they talking about? If an object (a book, let us say) is carried past behind them, and it casts a shadow on the wall, and a prisoner says "I see a book," what is he talking about?
He thinks he is talking about a book, but he is really talking about a shadow. But he uses the word "book." What does that refer to?
6. Plato gives his answer at line (515b2). The text here has puzzled many editors, and it has been frequently emended. The translation in Grube/Reeve gets the point correctly:
"And if they could talk to one another, don't you think they'd suppose that...