Translation
However, if I cast out demons by the Spirit of God, then the kingdom of God has come upon you.
Paraphrase
However, if I am casting out demons by the Spirit of God, that means God’s power to rule over human lives has confronted you, demanding that you decide between letting Him rule your life or ruling it yourself.
THE JEWISH CONCEPT OF THE HOLY SPIRIT
To understand this passage it is crucial to understand the Jewish concept of the Holy Spirit prior to the death and resurrection of Jesus.
The phrase “the spirit of God” was used in the Old Testament as the way in which God chose to reveal Himself. Usually, people saw God at work when He did something that man cannot do; this was the spirit of God at work. When Jesus mentioned the Holy Spirit in the passages given above, He was understood to be talking about the activity of God in the past. It was a reference to all the times that God had acted in obvious ways.
They would have thought of the way God revealed himself to Pharaoh through powerful plagues. This was the spirit of God at work. Likewise they would have thought of how God led them out of Egypt, including the crossing of the Red Sea. They would have recalled God’s provision in the desert where there is barely enough food for a goat, yet they were a population of over 600,000 men and their families.
Many other examples of the visible activity of God, or the spirit of God at work among men, would have come to mind as well. These would probably have included the crossing of the Jordan, the walls of Jericho falling down, David’s defeat of Goliath, the fire that came down from heaven onto the sacrifice at Mount Carmel, other miracles of Elijah and Elisha, the time Jehoshaphat defeated an enemy army by marching against them with a choir of singers as his front line, God’s protection of Daniel in the lion’s den, the way a hand wrote on the wall during King Belshazzar’s banquet, and the list could go on.
These were the things that were brought to mind by Jesus’ mention of the Holy Spirit. To them the term focused on the visible and obvious activity of God. Some would have also thought of the miracles Jesus had performed in their midst. They were all wondering, “Could this be the Messiah?” They were uncertain about His identity, but they could not deny the hand of God, i.e. the Spirit of God, that was at work through Him.