Jesus not only claimed that he was the Messiah and God incarnate; he also went at lengths to prove it. Even after having performed many miracles, including his own resurrection, the Jewish religious leaders still did not receive him.
Jesus understood that he had to demonstrate who he was. The synoptic gospels record Jesus as having forgiven the sins of a paralytic man. This alone is a right reserved for God alone. So, perhaps rightly so, the religious leaders accused Jesus of blasphemy. So Jesus said, “I will prove that I, the Son of Man, have the authority on earth to forgive sins” (Matt. 9:6). Then Jesus healed the man.
What this shows us is that Jesus used his miracles to prove that he was God in the flesh, and that he was given the authority by God the Father to do His work—forgive sins and to perform miracles—on earth. But this was not just to show his authority, it was also to show His compassion. 
Craig Blomberg explains further.
“When Jesus came to the synagogue in his home town, Nazareth, at the start of his Galilean ministry, he astounded his friends and family by his exposition of Isaiah 61:1, ‘The Spirit of the Lord is upon me, because he has anointed me to preach good news to the poor. He has sent me to proclaim release for the captives and recovery of sight for the blind’…Jesus’ preaching and healing are bound up inseparably with each other.’”
Note that this passage also references the Holy Spirit, who anointed Jesus to preach the good news to the poor. But because God is one, it is difficult to fully ascertain in the next sentence whether it was God the Father or God the Holy Spirit who sent Jesus (perhaps ekballo?) to do the work. Perhaps both sent Jesus out: the will of the Father; the prompting of the Holy Spirit.
In another miracle, the raising of Lazarus from the dead, Jesus explained that the death of Lazarus was to bring glory to God, for the people to see that Jesus was God, and that Jesus was sent by God the Father. When Jesus heard that Lazarus was dying, he said, “Lazarus’s sickness will not end in death. No, it is for the glory of God” (John 11: 4). Then, Jesus waited a few days to perform the miracle so there could be witnesses present.
But Jesus did not only perform this miracle for Lazarus’ family and friends; this miracle was also for Jesus to demonstrate to his own disciples who he was; “…this will give you another opportunity to believe in me” (John 11:15). When Jesus was about to raise Lazarus from the dead, he thanked God the Father loud enough for everyone to hear, “for the sake of all these people standing here, so they will believe you sent me” (John 11:42).
The miracles of Jesus are many, and it is evident with only a few examples that Jesus performed miracles to demonstrate that He is God, that He was sent by God the Father, worked with and through the Holy Spirit, and offered His compassion to all people.
 H. Wayne House, Chronological and Background Charts of the New Testament (Grand Rapids, MI: Zondervan, 1981), 98.
 James Jeffers, The Greco-Roman World of the New Testament Era (Downers Grove, IL: IVP, 1999), 45-46.