'The Peripatetics' (with a capital letter) were, literally, the students of Aristotle who walked around The Lyceum as they discussed philosophy. More recently, there are those who claim the name Peripatetics simply by following either the philosophy of Aristotle, or the rather free-style study methods thereof.
He helped push towards the Rennaisance by reintroducing the philosophy of Aristotle to the West. His writing used Aristotle's philosphy to interpret Christianity. This was a very materialistic philosophy, compared to the philosophy of Plato, which up to his time dominated Christian philosophy. (His sources were Jewish and Muslim thinkers from Spain who themselves rediscovered Aristotle.) So in short, he helped to shatter the medieval world-view, leading to the Rennaisance