What does Matthew 16:14 mean?

Jesus and His disciples are away from Galilee to the north. Jesus asks them who the people say that He is. Jesus seems to be probing to see if the people, and His own disciples, understand Him to be the Messiah.

The disciples respond that the people are divided in their opinions of who Jesus might be. Based on His teaching and miraculous healing abilities, many think Jesus represents the return or resurrection of one of Israel's prophets of old, like Elijah or Jeremiah. Others, including Herod Antipas (Matthew 14:2), believe Jesus to be John the Baptist somehow. Jesus has described John the Baptist as the fulfilment of the promise that Elijah would return (Matthew 11:13–14).

The disciples' response suggests the people who closely followed Him believed Jesus to be a powerful prophet of God. They saw in Him the fulfillment of prophecy. It's unclear what form, exactly, any of these separate groups expected the Messiah to take. The general assumption, in that era, was that Messiah would be a conquering warrior or political leader. Perhaps some thought the Messiah would be a prophet or would come to power after the return of the prophets. Very few, however, understood Jesus in the way Peter's view implies (Matthew 16:16).