John the baptizer had been laboring diligently to prepare the way for the Messiah when Jesus came to Him to be immersed (i.e., baptized). To John, it seemed to be too great an honor for him to baptize Jesus and too great a humiliation for Jesus to be baptized. Evidently, John was aware of Jesus' righteousness. Perhaps the reason why is because Jesus and John were relatives and knew each other--perhaps very well (cf. Luke 1:36ff). John tried to prevent Jesus from being baptized by saying - "I need to be baptized by You, and are You coming to me?" (Matt. 3:14). John's protest here needed to be made, for it spared Jesus from being baptized without explanation, as if he were a sinner. Baptism without such an explanation might have compromised, in the minds of some, the fact that Jesus was sinless.
Jesus said in Matthew 3:15 - "Permit it to be so now, for thus it is fitting for us to fulfill all righteousness." Jesus essentially told John, "Permit Me for this moment to appear as your inferior. The future will make the difference between us clear and plain, both as to our ministries and our natures." These words definitely show a Messianic consciousness on the part of Jesus.
Though John's baptism was not part of the Old Testament law, it was given by the authority of God, and thus Jesus would need to submit to it. If He didn't submit to John's baptism, then His conversation with the chief priests and elders would have been quite a bit different in Matthew 21:23-27! Also, this act was the divinely appointed method by which the Messiahship of Jesus was to be revealed to the witness John (cf. John 1:33,34).
After being persuaded, John did immerse Jesus in the Jordan River. John's humility caused him to initially object to this duty, but he did not continue to object. Humility ceases to be a virtue when it keeps one from performing his duty.
Matthew 3:16 says - "When He had been baptized, Jesus came up immediately from the water; and behold, the heavens were opened to Him, and he saw the Spirit of God descending like a dove and alighting upon Him." Immediately after His baptism, and as Jesus is praying, "heaven was opened" (Luke 3:21), and the Holy Spirit descended in bodily form like a dove (i.e., the Spirit was not an actual dove). It is reasonable to assume that at this moment Jesus received the ability to perform miracles by the power of the Holy Spirit (Acts 10:38). It should be noted that this is one of the few passages of Scripture where the three Persons of the Godhead are all mentioned.
In Matthew 3:17, this part of the narrative ends with the voice of the Father being heard from heaven - "This is My beloved Son, in whom I am well pleased." This announcement was the formal authentication of the Messiah's mission. He had been commissioned by the Father and anointed by the Holy Spirit (as prophesied in Isaiah 11:2; 42:1; 61:1). He was now ready to begin His public ministry for the redemption of man. It is interesting to note that Jesus was declared to be the Son of God at His baptism, and when one today is immersed for the forgiveness of his sins, he becomes a "son of God" by adoption (Gal. 3:26,27; 4:5).