Matthew’s gospel has been leading up to this question from the beginning: who is Jesus? (16:13-16). Jesus uses the title “son of man” several times in Matthew (see this on Matthew 10:23 for example).
Traveling to Caesarea Philippi, about 25 miles north of Bethsaida. The town was known as Panias, now Banias. Herod Philip built a Roman city on the site and renamed it to honor the Roman empire. One of the three headwaters for the Jordan river is in Caesarea Philippi. Matthew doesn’t tell us why Jesus and his disciples traveled to this location. The only thing that is important to Matthew is the dialogue between Jesus and the disciples.
While they are on the road, Jesus asks the disciples what the people are saying about him (v. 13-14). The question does not ask, “who do they think I am,” but “who the Son of Man is.” This sets the question in the context of Daniel 7:14, even if Jesus is using Son of Man to refer to himself.
The disciples offer several responses. Some in the crowds think Jesus might be John the Baptist, presumably raised from the dead. Others think he is Elijah who would come before the Messiah. This idea comes from Malachi 4:5, (see also Mark 6:15; Luke 9:8; Matt 17:10; Mark 9:11; John 1:21).
Still others think he might be one of the prophets, specifically Jeremiah. This is unique to Matthew, although in 2 Maccabees 15:12-16 Judas Maccabees has a vision of the righteous priest Onias and the prophet Jeremiah, who gives Judas a holy, golden sword as gift from God to strike down his enemies.
2 Maccabees 15:12–16 What he saw was this: Onias, who had been high priest, a noble and good man, of modest bearing and gentle manner, one who spoke fittingly and had been trained from childhood in all that belongs to excellence, was praying with outstretched hands for the whole body of the Jews. 13 Then in the same fashion another appeared, distinguished by his gray hair and dignity, and of marvelous majesty and authority. 14 And Onias spoke, saying, “This is a man who loves the family of Israel and prays much for the people and the holy city—Jeremiah, the prophet of God.” 15 Jeremiah stretched out his right hand and gave to Judas a golden sword, and as he gave it he addressed him thus: 16 “Take this holy sword, a gift from God, with which you will strike down your adversaries.”
In 2 Esdras 2:18 the Lord will send Jeremiah and Isaiah to the people when he opens the tombs and the dead rise from their places. Based on Deuteronomy 18:15–18, There was a Jewish messianic expectation that a great prophet like Moses would come at the time of the Messiah.
After hearing what the people are saying, Jesus asks, “but what about you?” Who do the disciples think the Son of Man is? Peter’s response is a turning point in the Gospel of Matthew, he declares that Jesus is the Christ, the Messiah, the son of the living God (16:16). In Matthew 12, the Pharisees decided who Jesus was, he is not the messiah and casts out demons by the power of Beelzebul. After this break with the Pharisees, Jesus begins to teach his disciples about the Kingdom of Heaven through parables (Matthew 13) and do a series of signs demonstrating to his disciples who he is, such as walking on the water (Matthew 14:22-33). Following Peters confession, Jesus will take three disciples up a mountain and God will reveal his glory and declare that Jesus is his beloved son (Matthew 17:1-13)
It is important to read Peter’s confession in the context of Second Temple Judaism: Christ is Messiah. This is the first time Jesus is identified as the Messiah in Matthew’s Gospel, although from the first line of the book Jesus is identified as the Messiah, the son of David. Although the title “son of man” does evoke a messianic passage (Daniel 7:14), Peter’s confession is the first time someone has specifically called Jesus the Messiah.
Peter also says Jesus is the “Son of the living God.” The king of Israel was like “son of God” (Psalm 2). In Matthew 14:33 the disciples confessed Jesus as the son of God. Nolland suggests the “disciples in the boat” (14:33) may not have included Peter (suggested by Nolland, Matthew, 665). 2 Samuel 23:1 also describes of David as anointed by God. “Living God” is a standard description of God in first century Judaism, that he is the “living God” means he is the real and only God.
It is possible this confession was something Matthew’s original readers would use in worship, although that is impossible to know for sure. In any event, after Peter’s confession that Jesus is the Messiah, Jesus begins to explain to his disciples the mission of the messiah, that he will go to Jerusalem and be killed and be raised on the third day.