For Plato an Idea was something objective, an intelligible archetype. The Christian Platonists replaced the archetypes with inborn memories, which they call innate ideas. The possession of these innate ideas and reflection upon them are necessary conditions for obtaining necessary truths.
[from Greek idea, what a thing looks like, in turn from idein, to see, to look, a declension of eidein, to see, to look, from which comes eidos, form, the synonym of idea]
Plato used idea and eidos interchangeably for the non-sensible entities that are unchanging, eternal, and universal absolutes, the objects of knowledge, and the paradigms from which sensible things derive their reality. He held that these supreme entities are the essence or inner structure of things. The transition of idea from outer look or shape to inner structure is by way of a metaphor. If you see with eyes, what you see is outer shape, but if you “see” with the soul – that is, think – what you get is essence or the common characteristic. Platonic ideas are objective, in contrast to ideas as subjective, mental ideas in modern philosophy. To avoid confusion, many modern scholars prefer to call Plato’s doctrine the Theory of Forms rather than the Theory of Ideas.
“You remember then that I did not ask you to indicate to me one or two of the many pious actions, but the very Form (eidos) itself by which all pious acts are pious. For you said, I think, that it is by one Idea (idea) that impious things are impious and pious pious.” Plato, Euthyphro