John the Baptist had been baptizing people from Jerusalem, across Judea, and throughout the region where the Jordan river ran. He was calling people to repentance from their sins, preparing the way for Jesus to come, the one who would save them from their sins and call the people into his Kingdom.
But then Jesus comes to John to be baptized. John is, at first, reluctant to baptize Jesus, but Jesus says that they must do it to fulfill righteousness. It is important that Jesus also be baptized, leading the way for the people to be baptized in his name in the future.
As Jesus is baptized, he comes back up out of the water and we read about two amazing things that happened:
The heavens were opened to him, and he saw the Spirit of God descending like a dove and coming to rest on him; and behold, a voice from heaven said, “This is my beloved Son, with whom I am well pleased.”Matthew 3:16-17
Jesus is immediately met by the Spirit of God descending upon him. We see the Spirit entering Jesus, confirming his identity as fully God. Jesus was born without a human father, of a virgin birth as the result of the Spirit placing Jesus within Mary, but now we see the public entrance of the Spirit within Jesus confirming his identity as both a full human as well as fully being God.
After this, we also see that God speaks from heaven about Jesus saying that Jesus is His Son, and He is pleased with him. God the Father identifies Jesus as His Son. He says that Jesus is, in fact, divine. He comes from heaven. He comes from God. God has confirmed that Jesus is the Christ, the Messiah, the One who would carry out God’s plan here on the earth.
So in this one scene, we see all three persons, all three representations of God, all at work in one place at one time.