What is the significance of Friday the 13th according to this section of the book?

The significance of Friday the 13th in this section of the book is that Langdon explains more to Sophie about the Priory of Sion. The Priory is protecting secrets known as the Holy Grail, which, according to Langdon, is not a cup at all. Also, Sophie learns that during one of the Church's campaigns to seize the documents and secrets of the Priory, they launch a sting operation on Friday, October 13, 1307. Countless Knights are captured and tortured on that day, which is why Friday the 13th is considered unlucky to modern day.