Theory of Forms

Read this description of Plato's theory of the forms. What does Plato mean by "forms"?; How does this relate to justice? What does the ideal state have to do with justice?

We call both the sky and blue jeans by the same color, blue. However, clearly a pair of jeans and the sky are not the same color; moreover, the wavelengths of light refracted by the sky at every location and all the millions of blue jeans in every state of fading constantly change, and yet we somehow have a consensus of the basic form Blueness as it applies to them. Says Plato:

But if the very nature of knowledge changes, at the time when the change occurs there will be no knowledge, and, according to this view, there will be no one to know and nothing to be known: but if that which knows and that which is known exist ever, and the beautiful and the good and every other thing also exist, then I do not think that they can resemble a process of flux, as we were just now supposing.

Plato believed that long before our bodies ever existed, our souls existed and inhabited heaven, where they became directly acquainted with the forms themselves. Real knowledge, to him, was knowledge of the forms. But knowledge of the forms cannot be gained through sensory experience because the forms are not in the physical world. Therefore, our real knowledge of the forms must be the memory of our initial acquaintance with the forms in heaven. Therefore, what we seem to learn is in fact just remembering.