The official start of the physical ministry of Jesus can be seen in Matthew 3. When John the Baptizer was doing his work in the wilderness, he pointed people to the one who would come after him. One day John saw Jesus coming to him for baptism. From this request John stated that he needed to be baptized by Him, not the other way around. Jesus said that is was to be done to fulfill all righteousness, and thus John baptized Jesus. After this the people that were there saw the Holy Spirit descend in the form of a dove and the Father spoke from heaven identifying Jesus as His Son. This is a wonderful event to begin the ministry of Christ for Him to teach, perform miracles, and eventually give His life as the sacrifice of God.
But it begs the question, why was Jesus baptized? We know that John’s baptism was of repentance for remission of sins, but Jesus didn't need to repent of sin since He was sinless (1 Peter 2:22). So why then was Jesus baptized? There is not a conclusive answer in scripture besides “to fulfill all righteousness”, but there is one prevalent thought which is interesting.
The time from Jesus’ ministry to His crucifixion were a time of transition. John was preparing the way for Jesus’ work, the law of Moses was coming to a close, and what mankind would have to do to be righteous before God was changing. There would be no more need for animal sacrifices, nor solemn feast days. The idea of believing the message of God, repenting of a sinful lifestyle, confessing Jesus in the same way the Father spoke from heaven, and then being immersed in water to be cleansed from sin was a new thing. John introduced a form of baptism, which is distinct from the baptism of the gospel (Acts 18:6). This prepared people for the transition that was coming in the next three years.
So again, why was Jesus baptized if not for repentance? It may be that Jesus began his ministry by being an example. He didn't need to repent of sin, but His baptism prepared people to learn from Him that there is something new happening that begins with baptism. In other words, Jesus was baptized to signify the importance of being baptized to be a follower of Him. If we want to follow in His footsteps, we might be confused if we must do something He never did. So what is the application? Jesus began his work the right way. Ever mindful of what His followers would learn and think and do. What a blessing it is to know our Lord cares for us to this extent.