The Kingdom of God means primarily the rule of God, the divine kingly authority. There is no difference between the Kingdom of God and the Kingdom of heaven. These terms are linguistic variations of the same idea. There is a hostile kingdom, the Kingdom of this world which is under satanic control.
The purpose of Christ's reign is to destroy all hostile forces and to subject all to the rule of the Divine Sovereign. The purpose of the Holy Ghost is to take out of you this hostility and worldly way of thinking and living. The last enemy to be destroyed will be death. When all has been brought under the rule and dominion of the Father, the office of the Sonship will cease, for it will have accomplished its purpose.