Platonic describes a relationship that is not sexual. It is often used to describe friendships or relationships that are not romantic or sexual in nature. The term platonic finds its origins in Plato's "Symposium" where it is explained in reference to the term Divine Eros or divine love which is love that transcends the physical body.
In its modern use, the term platonic is often employed to describe friendships between people. Much debate rages over the ability of men and women to maintain platonic relationships in the face of sexual tension and romantic inclination.