For me the purpose of this allegory is the process of enlightenment and the explanation of the education of the soul in becoming wise.
In the Allegory of the Cave the predicatment in which mankind finds itself is described symbolically. The Allegory also present Plato's major philosophical assumptions: his belief that the world we conceive through our senses is not the reality yet a poor copy of it and reality can only be reached intellectually, not just learning knowledge but gaining wisdom.
In the first part of the Allegory an underground cave is described; called "the prison cave" or more metaphorically "the unenlightened world". In this cave, people or prisoners (as they are called) are chained to the cave wall so they cannot move at all. A fire is above them and behind them. The fire throws images on the wall opposite the prisoners. Another wall separates the prisoners from the fire and the guards near the fire. They can only see
They just stay content with their world. Yet when the prison house is being described they so not say the prisoners are discontent, but rather comfortable with their current reality. You can realte the Allegory to human kind's natural reaction to change. He was at the bottom of the latter, knowledge, and now is working his way up to wisdom. Just like the prisoner could not look at the bright sun. In the beginning we are reluctant to accept these changes. All together the Allegory is the idea that mankind relies upon our observations to know the truth about the world, or reality itself which in fact we know little about. After the prisoner ascents out of the prison cave he is in the enlightened world. It is painful for him because his eyes cannot handle it. Hence why the gaining of wisdom is gradual. sometimes the guards speak and the prisoner believe that the shadows are speaking. In this way the cave, or prison house, is representative of the world of sight. before them their own shadows and the shadows of other prisoners. With this come many changes; to us and the world around us.