What does Matthew 16:13 mean?

Jesus and His disciples have crossed the Sea of Galilee once more (Matthew 16:5) but this time they travel together 25 miles north of Galilee to the district of Caesarea Philippi. The town, at the base of snow-capped Mount Hermon, had previously been dedicated to the worship of Baal and then to the Greek god Pan. Now it had been enlarged and renamed by Herod the Tetrarch in honor of the Roman Caesar, with "Philippi" added to keep it from being confused with the coastal town of Caesarea. The region was now populated mostly by Gentiles. Jesus may have travelled there to be away from Galilee and to focus His attention on His disciples.

Christ begins this exchange by asking His disciples about what they've heard from others about who the Son of Man is. "Son of Man" is the name Jesus most often used for Himself. The name not only emphasized His humanity, it was a clear reference to a prophecy about the Messiah in Daniel 7:13–14. Daniel describes one like a "son of man" who was given "dominion and glory and a kingdom, that all peoples, nations, and languages should serve him" (Daniel 7:14).