In the philosophy of Plato, Forms (or Ideas) are abstract, perfect, unchanging concepts that constitute what is ultimately real. The objects that we see in the world around us—the world of time and space—are but copies of some higher, deeper reality. In other words, they are copies of the Forms rather than the Forms themselves. As such, an investigation of the spatio-temporal world cannot provide us with the truth. Only a rational comprehension of the Forms can do that.

Plato illustrates this point with his famous allegory of the cave. The men who have been chained up their whole lives in the cave can only see the shadows of men appearing on the wall. As they have never seen actual men before, they take the shadows for the reality.

This is the position that most people—i.e., people who are not philosophers—take in relation to the spatio-temporal world. They look around them and see a world of objects, which they unthinkingly regard as constituting what is ultimately real. But in truth, they are only seeing the shadow of some higher reality—the reality of the Forms. Just as the men chained up in the allegory of the cave mistake shadows of men for men themselves, so the vast majority of humankind mistakes the world of objects for what is ultimately real.

The allegory of the cave is probably the most famous of all the passages in the Republic. It is used to show the difference between the world of senses and the world of forms. Forms are immutable and timeless, unlike what we see/feel/sense in the actual world, which are shadowy, unreliable reflections of their Forms. Plato believes that humans can never really see the Forms, but there are some that are able to apprehend them more clearly than others.

The allegory he uses in the cave is that the prisoners who are chained to the wall and forced to watch the shadowy figures and scenes that can be seen through a curtain—the shadowy figures (which we know are not real) become their view of reality.

If a prisoner was released and forced to see the "real" world as we know it, the brilliance of it would be painful and difficult for the prisoner to understand. At first, the man would want to return to the cave and the comfort of his own reality, but once he became used to it, he would eventually realize that he had been living a life of illusion in a world in which he didn't even know that the sun existed. He may go back and try to teach his fellow prisoners about his new reality, but if he attempted to release them to experience what they would see as madness, they would try to kill him.

Plato uses this allegory to explain why philosophers are so often mocked: they have had a glimpse of the Forms, and the people to whom they are trying to explain those ideas find them incomprehensible. Most people are stuck in the shadowy world of the senses, like the prisoners in the cave.