He is asking Jesus, "Be specific about this charge. Be specific in your answer regarding this. Are you a king?" And Jesus' answer ought to be very clear to you and me.
Now remember that we are pursing the subject of the announcement of the Kingdom of God and the entering into the New Covenant, and the subject of government. How does it apply to you and me now—in the church, in the twentieth century here? "My kingdom is not of this world."—meaning age, meaning system of things. It is the Greek word cosmos. It is not of this system. That is, Satan's system!
Jesus was, in effect, saying to Pilate, "My Kingdom is better." Mainly, what He is talking about here is the nature of His reign, the nature of His rule. Not its location, or its time. Remember that He refused to give even His disciples an indication of time. He certainly was not going to give it to Pilate. However, that can be included in the understanding of the verse, but it is not primary.
Jesus is concerned about the nature of the Kingdom here. What He was telling Pilate is, "Pilate, My Kingdom isn't political. You have nothing to worry about from Me. I'm not here to overthrow the government and establish a competing power before you." So He is saying then, "I am not a rival. I'm not here for political reasons." If He had been, what would His servants have been doing? They would have been making war.
When we put this together with other verses, we can understand that Jesus is saying—to you and me—that, "My Kingdom is spiritual! It is, indeed, beginning now." He says, "I am a King!" You are not a king over nothing. He was a king over something; and that Kingdom was beginning. But its installation as a power on this earth was not yet. We are talking about something that is not, at this time, a rival to governing authorities.