Matthew 3:13-17 - Baptism of Jesus

John has just finished telling people how great is the One who will come after him, then a most surprising things happens. Jesus arrives and asks to be baptised by John. Remember how John greeted the Pharisees and Sadducees (v7), indeed in Luke's account it is apparent that calling people a brood of vipers was John's default greeting! John knew that his baptism was a baptism of repentance. It was for sinners, for people who needed to change their heart and their ways. Then the Messiah comes along and He insists on being baptised! 

This posed a deep theological quandary for John and he responded initially be trying to deter Jesus from being baptised. We cannot put God in a box, His ways will always surprise and shock us at some point (remember how Peter reacted when Jesus told him He must die).

Why did Jesus need to be baptised? He was standing as the representative of all mankind, He was going to go to the cross as a sacrifice for everyone. So He needed to be baptised. John then agreed to do this.

After He was baptised the Holy Spirit descended upon Jesus like a dove, and a voice from heaven declared that "this is my Son, whom I love, with Him I am well pleased". Matthew is showing that Jesus was anointed by the Father, and was approved by Him.
As an aside, this is one of many places in the Bible where we see Father, Son and Holy Spirit together, ie all three persons of the trinity. Some people object that the Trinity is not found in the Bible. This is nonsense. The word "trinity" is not found in the Bible, but the doctrine of the Trinity encapsulates what the Bible teaches about the relationship between the Father, Son and Holy Spirit.