It is after Jesus' baptism that we model our own way of baptizing. It says "he came up out of the water" (Matthew 3:16) showing that he was dunked into the water and brought back up. This symbolizes the death and resurrection that would be coming in his life. He would be buried and then rise again cleansing the sins of the world.
After his baptism we see the other two members of the Trinity enter the scene. The Holy Spirit falls upon him empowering him for the work of ministry he is about to start. The Father speaks from heaven affirming that Jesus is indeed his beloved Son. Jesus is now prepared to begin his ministry.
Baptism represents our confession that we are sinners and need Jesus to cleanse us. It is a public declaration that our life is no longer our own but belongs to God. We a dunked under the water representing our death to our previous life, our life of sin. We are the brought out of the water representing our resurrection with Jesus and our new self, our new life which belongs to the service of God.