Plato and Aristotle were immensely influential figures in Greek and Roman philosophy. Christianity could not escape their heritage which has characterized much of western philosophy and science for more than two millennia. [TheHermit - to our great cost]
The most influential notion which came from Greek Philosophy to Christianity is that of Platonic Idealism. This approach to the nature of human perception and reality undergirds the development of Christian theology in a fundamental manner. To fail to understand Plato's doctrine of Forms and the development of Platonic Idealism in the Middle Ages into the doctrine of Realism is to fail to be able to interpret the Christian message in its doctrinal formulations. The influence of Platonism was really challenged only in the Middle Ages by the philosophy of Aristotle and the development of Nominalism.
The best description of Platonic Idealism (also called Platonic Realism) and its emphasis on the notion of mental illumination is given by Plato himself in Book VI of The Republic. The Myth of the Cave is the classic exposition of Plato's thought.
Plato's idealism went a step further. He understood that genuine reality had to emerge from unity or from a universal. He strove to maintain this principle of unity and did this by suggesting that the essence or essential aspect of all classifications and all objects were united in the Unity of Being. He called these essences which became objective to us in phenomenal Ideas or Forms (Ideai or eide). For Plato these Forms or Ideas were the objective content of our universal concepts. Thus the sensible things we feel, measure, and experience are the objects of science and human experience. These Forms are temporal and mutable (changeable) while the original essence is perfect, eternal and unchangeable. We shall see later that these Platonic categories had great influence on those who formulated heretical statements as well as the response to those statements later adopted by the councils of the Church.
The Unity or The One from which all the Ideas emanated was The Good, according to Plato, who thus brought together The One, The Good and essential Beauty from which came the intelligible or sensible world of Forms. But the word "emanation" was not used by Plato himself. This concept came from the Neo-Platonists, those followers of Plato who lived just after Jesus. The concept of emanations was taken by Gnostic and Christian theologians from the Newplatonists.
TheHermit <shuddering gently at the idea that somebody imagined that he might fall for this lame idea>