Like many School of Life videos, the above is a great introduction to the story and background to what is known as the "Allegory" of Plato's cave. I appreciate their effort, and love their work, but like most philosophy students steeped in western thinking they hear and see and mouth the words but pull back in fear, and make academic rationalizations about the exhortation to practice philosophy as the solution to our captivity. In the gentle, but not so socratic method outlined above, they settle on the teaching and practice of western philosophy as the intent of the story, and completely miss the point. The Neo-Platonic philosophers knew the answer and it is Find the Exits. Plato had been trying to convince people of the existence of a higher world and the particulars of the ideal forms that reside above. He knew he sounded like a lunatic, but luckily he was an interesting enough lunatic that people preserved his thoughts. The irony is that we remember his best effort at making this clear as an allegory, when it is a statement of absolute fact.
You are looking at the shadows projected from the higher reality, all the real and better stuff is behind you and you have no idea how to turn around and look because your perceptions are chained forward looking away from the source. It is the tragedy of philosophy that Plato could not leave a training program for escaping the cave, but instead just hinted that maybe you are not perceiving enough. The story is a treasure of the ages, but go further. The Kabbalists actually went there and drew a map if you are interested in getting closer to the truth. The map has hints and pictures, but in order to follow it you have to have a spiritual practice, not discourse in the town square. Turn your perception above and behind you. Everything in front of your eyes exists in the 4 lowest dimensions and through a trick of refraction the higher 6 dimensions appear invisible. They are not. Sit, meditate, and search inside your head for the bit of sunshine peeking in. Follow it out to freedom.