Plato's theory of forms
Plato's theory of forms holds that beyond the physical world we perceive with our senses, there exists a realm of perfect, unchanging forms that physical things only imitate or participate in. A particular beautiful object is beautiful because it partakes in the form of Beauty itself; a triangle drawn on paper is only ever an approximation of the perfect form of Triangle. Knowledge of the forms comes through reason, not the senses, which is why Plato ranks philosophical understanding above ordinary perception.
Why it matters
It sets up a divide between appearance and reality that runs through the rest of Western philosophy, and it explains why Plato trusts reason over the senses.