What does Matthew 9:34 mean?

Scripture never presents miracles as routine, common, or ordinary. Miracles are intended to be "impossible" events which can only be explained by the intervention of God. In particular, they are meant to support or provide some kind of message. This is why the New Testament often refers to such acts as "signs" (John 6:14; 20:30–31). Like any other evidence, however, signs can be ignored or misinterpreted. Members of Israel's Jewish religious leaders were present at many of Jesus' healings and stood before Him as He taught. This includes the especially-religious group known as the Pharisees.

In spite of being eyewitnesses to Jesus' undeniable displays of power in healing the sick, casting out demons, and even raising the dead, the Pharisees refused to believe what others had come to: that Jesus was the Messiah, the long-promised Son of David, arrived at last to save Israel.

In order to reject that conclusion, the Pharisees need to explain the power behind Jesus' miracles in some other way. Having seen Him cast out another demon in the previous verse, the Pharisees present declared that He casts out demons by the prince of demons. By this they meant that Satan was the power source behind Jesus' easy command over the demons and perhaps the power behind His other miracles, as well.

A notable exception to this conclusion among the Pharisees was a Pharisee named Nicodemus. He came to Jesus under the cover of darkness and admitted, "Rabbi, we know that you are a teacher come from God, for no one can do these signs that you do unless God is with him" (John 3:2).