The prisoners are mankind before they are given the chance to gain knowledge. They know only what they have seen and believe that is reality because there is nothing to suggest otherwise. They are unable to turn their heads because of the chains that hold them there. The chains are their belief that what they see MUST be reality, preventing them from seeing any other possible reality. The shadows are their false truths of what is real according to Plato.
The upperworld is the world gained of knowledge. It's different from anything the prisoners have known before. The light is the knowledge they are being presented with and gaining. The sun is the provider of knowledge similar to how the sun provides light.