For Plato there are two words; the eternal world and the material world. The eternal world possesses the object of knowledge and is more real than the material world which possesses the object of opinion.
State of Flux
The material world when it is in a constant state of flux and therefore it is impossible to know the truth of reality - “You cannot step into the same river twice”.
The Realm of Ideals
Perfect forms exist in the realm of ideals or forms, which possess the object of knowledge. Sense perceptions of material objects are simply objects of opinion, subject to constant change. Knowledge is innate, a recollection of the perfect forms.
“Her eyes are too close together” – we can recognize that she falls short of beauty and thus understand the concept of beauty, yet we have not ever experienced a perfect example of beauty.
We have concepts of the perfect forms thus our souls must have known them before we were born (innate, ‘a priori’ knowledge) –evidence that we have immortal souls.
A circle is a 2D figure made up of an infinite series of points all the same distance from the centre. No one has ever seen the perfect form of a circle but instead imperfect copies, reasonable approximations of the true form. A perfect circle could not be seen or drawn even if one used the most sophisticated computer equipment. This is because, in its perfect form, the infinite numbers of points which make up the circumference don’t take up any space as they exist in logic rather than physical form. Yet although the perfect circle can never be seen, people can define a circle from their soul’s recollection of the true form from the realm of ideas.
Forms give physical objects what reality they have because of their resemblance. The shadows in the Allegory of the Cave only had any kind of existence because of their resemblance to their corresponding physical objects.
Goodness is the most important form. Like the sun in the Allegory of the Cave, Good illuminates all the other forms. Justice for example is an aspect of Goodness.