From The Gospel of Matthew by Curtis Mitch and Edward Sri, commenting on Matthew 16:13-20:
The exchange between Jesus and Peter at Caesarea Philippi is the climax of the first half of Matthew’s gospel. From Peter we hear the definitive declaration that Jesus is the Messiah of Jewish expectation and the Son of the living God. In return, Jesus issues his own declaration that Peter is to be the foundation of a new and messianic temple known as the Church. The constellation of images and themes that appear in this dialogue are closely linked to the Davidic covenant and its attendant traditions.