Theory developed by Plato (c.427-c.347 BC) in his middle-period dialogues (especially Phaedo, Symposium, Republic) and criticized by himself in his Parmenides (see third man argument). The language of the theory occurs in his earlier dialogues, but its interpretation is disputed, as is his reaction in later dialogues to the Parmenides criticisms: did he modify the theory, abandon it, or treat the criticisms as applying only to a distorted version of it?
Forms (usually given a capital F) were properties or essences of things, treated as non-material abstract, but substantial, entities. They were eternal, changeless, supremely real, and independent of ordinary objects which had their being and properties by 'participating' in them.
But Plato puzzlingly treated them as both universals (see Platonism), suggesting they were immanent in things, and paradigms (see paradigmatism), suggesting they were transcendent and themselves had the properties they represented: Beauty is beautiful (but Change changes - despite being, as a Form, unchanging). Aristotle (384-322 BC) too believed in forms (with a small F), but no longer as transcendent objects. 'Idea' is a misleading synonym for 'Form'; Forms were objects of knowledge but in no way themselves mental or in the mind.
Also see: one over many principle
W D Ross, Plato's Theory of Ideas (1951)