This miracle that Jesus performs he uses to call out the Pharisees. Jesus was the hardest on the Pharisees probably because they were the closest religious leaders to himself. They believed that the Messiah would one day come, they followed and kept the law, and they believed in the resurrection of the dead (the other religious leaders, Sadducees, didn't believe that). But the Pharisees lacked compassion for people and held the law above all else. This obsession with the law was keeping them from seeing God work and so Jesus uses the healing of the blind man to try and open their eyes.
In Ancient Israel, any disablility; blindness, leprosy, etc; was thought to have been caused by sin. In the case of this man, who was born blind, they wondered if it was the sin of his parents that caused them to have a blind child or whether it was punishment for the man's own sin given out before the offence. Jesus said it was neither but it occurred so that god may be glorified. There is pain and suffering because of sin entering the world but God can use that pain and suffering for glorious things.
The Pharisees have had enough of this blasphemous man who claims to be the Son of God. They want to get rid of Jesus and so they question the blind man. They are so focused on the law being followed that they ignore the fact that this man born blind can miraculously see, something that has never occurred before. They first don't believe the man was blind in the first place but evidence is shown that it was true. Instead of being amazed by this and praising God they focus on the fact that Jesus healed on the Sabbath and broke the law. The blind man corrects them and says, "I don't know whether or not he is a sinner but I do know that he healed me, and that is a miracle." He had the right perspective.
Jesus then point it's attention to the Pharisees during one of his teachings. The Pharisees should know that Jesus is the Messiah because of their great knowledge of Scripture that all points to Jesus. The Pharisees believe they can see the Messiah and thus say that Jesus is not. Jesus tells them that if they knew nothing of Scripture they could plead ignorance but because they know Scripture so well and claim to know all they have no excuse for missing the Messiah standing in front of them.