What is the Priory of Sion, according to Langdon, and how does it play a role in the story?

According to Langdon, the Priory of Sion is a secret society which included members such as Boticelli, Sir Isaac Newton, Victor Hugo, and, of course, Leonardo da Vinci. The group is well known for worshiping the sacred feminine, known as the cult of pagan goddess worship. Langdon believes that Jacques was a member of the Priory, based on the event that Sophie witnessed that caused the rift between herself and her grandfather.