Platonic is an adjective that suggests the idea being described comes directly from Plato's works or indirectly from Plato's ideas.
Several key uses of the term platonic include: Platonic love, Platonic philosophy, Platonic idealism, and Platonic economics.
Platonic love is focused on the idea of forms, which translated into modern love simply mean emphasizing the spiritual or idealistic rather than physical or materialistic. For example, two men can share platonic love for each other if they are siblings, extremely close friends, or a "father/son" type relationship of two unrelated men, the younger of whom learns from the older as a role model. Older married couples often find their relationships become platonic as they emphasize the spiritual part of their lives rather than the sexual or physical.
Platonic friendship is a close but non-sexual affection between people of different genders. In other words, it is being good friends rather than lovers.
Platonic philosophy is the branch of philosohpy that derives from Plato's world views, and includes focus on the Forms, focus on a three leveled view of government (Head, Body, Heart; Philosophier/King, Military, Workers and advisers).
Platonic Idealism defines the entire world as imperfect shadows of the perfect Forms. Some people see connections between the idea of a perfect Heaven with Platonic Idealism. That Christians strive to be as close to perfection as possible, knowing it can never be achieved on this Earth.