What is Plato trying to teach with his allegory of the cave?

Plato's allegory of the cave is a story that comprises of a few parts that are meant to be compared to the real world . The story, simply, is about some captives who's only experience of seeing things in the shadows they make on the wall - as they are chained such that they can only see the wall and not the things behind them casting the shadows. One captive then breaks out of the chains and ventures outside. The key elements here are the captives, the chains, the shadows, and the outside.The captives are meant to represent individuals - some stay captive and other break out, these are the philosophers. The chains are comparative to the person's intellect and whether or not one can break from what is expected of them. The shadows are the things that we see every day, this is all we really know. The outside world, then, represents the larger "world of forms" that Plato thought that philosophers would find if they are inquisitive enough. The allegory is attempting to show the 'layman' the value of learning philosophy as most people don't consider the complex world of the 'unseen' and in this circumstance, the theory of forms. This leads neatly into some of his other works that suggest humans have a certain innate knowledge that we simply need to unlock, ect.