What is Plato's 'Theory of Forms'?

Plato's Theory of Forms is an epistemological response to the nature of reality. This means Plato attempts to answer the question 'what is true reality?'. The idea is that every object in the world we see, is a less-perfect copy of an ideal object found in a world Plato calls the 'Realm of the Forms'. Our souls have visited the Realm of the Forms before entering our bodies and so this is how we can identify common objects such as a 'chair' or a 'cat'. 

Plato puts forward the 'cave analogy' to emphasise his theory of Forms. In this, the 'cave' represents the world we live in (a world Plato calls 'world of appearances'), and prisoners that are chained up represent trapped humanity. The prisoners are facing a wall where they can see shadows of objects they believe to be real, and in order to truely understand the shadows one has to escape and make the journey out of the cave. When a prisoner leaves the cave they will see true reality in the form of the outside world and so have sought true knowledge. This supports Plato's Theory of Forms because it shows that an escaped prisoner can understand his reality, much like we as individuals can understand our world as long as we continue to pursue philosophical knowledge.