What does Matthew 3:13 mean?

Matthew now introduces Jesus, the subject of his gospel, for the first time as an adult. When last we heard of Him in the gospel of Matthew, Jesus was a small child living in the disreputable town of Nazareth in Galilee (Matthew 2:19–23). His parents had settled there to keep their distance from Jerusalem and the region of Judea, where a former king had tried to kill Jesus as a baby (Matthew 2:13–16).

Since Jesus arrives on the scene from Galilee at around 30 years old, most scholars assume that He had lived in Galilee up until this point in his life. He finds John preaching and baptizing somewhere along the Jordan River. Jesus wants John to baptize Him.

We know from Luke that John and Jesus were extended family through their mothers; Mary and John's mother Elizabeth were related (Luke 1:36). Both men were born by the intervention of God. Jesus, of course, was conceived by the Holy Spirit, making Him the Son of God, the long-promised Messiah. John's birth was also predicted to his father, Zechariah, by an angel. This was despite the married couple being past the normal age of having children. The angel told Zechariah that John would do exactly the work Matthew has described of him so far. John would "make ready for the Lord a people prepared" (Luke 1:17).

Now the Lord Jesus Christ and John meet face to face in an unexpected way. That is, John did not expect this request from Jesus.