The analogy is allegorical therefore different parts of the story are symbolic to situations we as people can face.
The cave represents the visible world we live in, the realm of appearances, however Plato seems to suggest that the prisoners represent ordinary people (such as us) who have not yet experienced true knowledge. Therefore have only discovered the false reality in the cave, including the shadows being cast on the wall. These shadows represent the illusions we see every day, they are the imperfect interpretations of the ideal form. To the prisoners they are real they exhibit structure so the sights and sounds seem real, this corresponds with us. Plato emphasises that the illusions are misconceived, and describes shadows as being artificial objects created by the fire.
Plato uses the prisoners and the cave as a way of explaining to people that we, like the prisoners, do not know the truth but believe that what we see is reality however only philosophers know the truth (the realm of the forms). The cave is also used to suggest how the human body deceives us by imprisoning the soul and providing us with illusions from our senses. Plato says that these illusions seem more reliable that realty therefore the body stops the soul from looking for true knowledge (philosopher discovering the realm of the forms/form of good).
Before the prisoner could leave the cave, he had to loosen his chains to escape. This is equivalent to a philosopher as they must free themselves from the illusion created by their own senses by using their brain to gain truthful knowledge. Therefore the journey out of the cave into the intelligible world represents a philosophers discovery of true knowledge. Plato often emphasised that this journey would be painful and confusing because it would involve the philosopher dismissing everything he had ever known.
The forms are different to concepts and objects within the intelligible world because the forms must be completely consistent, therefore infinite and unchanging. Whereas particulars depend on their physical state and are changeable and imperfect.
Although we cannot see or feel the forms they are still relevant to us, Plato believed that the resemblance of items to it’s perfect form is the only reason why we can recognise and classify things in the visible world. For example dogs come in different sizes, colours and shapes however classify them as the same thing, a dog. Plato said that we do this because they all share the Form of a dog, which we have experienced through our immortal soul before we entered the realm of appearances. Therefore we have innate knowledge of the ‘ideal’ dog that can be developed through rational thoughts that lead to the soul remembering these memories (this process is called anamnesis).
Plato believed that the most important form was the form of good, which he said was the central existence of the whole universe, without this form there would be no ideal form of beauty or justice etc. The different forms all connect together with a fixed order of importance, created by the form of good as it gives each forms its own nature.
In the Analogy of the cave the sun represents the form of good, the sun gives light to illuminate the objects that it is giving life. This corresponds with the Form of Good as it gives us knowledge of all the other forms. Only king philosophers can gain knowledge of the Form of the Good as it will lead to full understanding of everything, this is what drive Plato to argue that many philosophers and politicians should not be leading society as they have not yet gained full and true knowledge of the forms.
In conclusion Plato uses parts of the analogy as symbols to represent how his theory is relevant to us. For example when the philosopher was being dragged out of the cave and looked into the light, he experienced pain and struggled. This shows that gaining knowledge of the truth would be distressing and may force a person to change their views during the hard process. Plato uses The Analogy of the Cave to show that what we believe to be reality is in fact imperfect shadows of the ideal forms and that only by becoming a philosopher can we gain the true knowledge.