Platonic is an adjective used to refer to the Greek philosopher and mathematician Plato. Popularly, the term Platonic came to be used with the meaning of something ideal or chaste, without material interests. For example, a platonic love is one that is only on the spiritual plane, without carnal or sexual contact.
Plato lived in Athens about 400 years before Christ and created a philosophical theory called the Theory of Ideas, or Theory of Forms. According to this theory, the world is divided into two parts: the World of Ideas, in which the idea of things is perfect, and the Sensitive World, where there is only a partial perception of things through the senses.
In one of his most famous texts, The Allegory of the Cave, Plato presents an allegory in which a group of people finds themselves trapped inside a cave with no view to the outside. These prisoners only have a partial idea of the real objects out there through the shadows cast in the cave by the light of a fire.