This important question is at the center of much theological discussion these days, and in their book What is the Mission of the Church? Kevin DeYoung and Greg Gilbert state their own case for what exactly the kingdom of God is. Here’s an excerpt from the book:
You cannot ‘expand the kingdom’ by bringing peace and order and justice to a certain area of the world. Good deeds are good, but they don’t broaden the borders of the kingdom. The only way the kingdom of God–the redemptive rule of God–is extended is when he brings another sinner to renounce sin and self-righteousness and bow his knee to King Jesus. (121)
Essentially, DeYoung and Gilbert argue that the ‘kingdom’ spoken of constantly in the New Testament is not a geographical term, but rather a relational term. Unlike popular ‘Christian activism,’ DeYoung and Gilbert argue that this kingdom of God is exclusive to those in the church.
While I disagree with their interpretation of the Old Testament in the same way (the Old Testament certainly places great emphasis on the role of the land in the kingdom of God and it is not until the coming of Jesus that people are able to worship neither on this mountain or the next but rather in spirit and in truth [cf. Jn. 4:21-24]), I think that they hit the nail on the head. There is plenty of biblical evidence for this point of view:
In John the Baptist’s and Jesus’ proclamation of the coming kingdom, this arrival of the kingdom is a cause for repentance–you cannot enter the kingdom without repentance (cf. Mt. 3:2; 4:17; and parallels).
Col. 1:13 He has delivered us from the domain of darkness and transferred us to the kingdom of his beloved Son
1Cor. 6:9 Or do you not know that the unrighteous will not inherit the kingdom of God? Do not be deceived: neither the sexually immoral, nor idolaters, nor adulterers, nor men who practice homosexuality, 10 nor thieves, nor the greedy, nor drunkards, nor revilers, nor swindlers will inherit the kingdom of God. (and similar passages)
1Th. 2:12 we exhorted each one of you and encouraged you and charged you to walk in a manner worthy of God, who calls you into his own kingdom and glory.
‘Kingdom’ is mentioned 154 times in the New Testament, and of those that refer to the kingdom of God (either explicitly or implicitly), they all best fit into this framework. This is not an excuse to stop seeking justice in this world, but it is important to realize that, as DeYoung and Gilbert say above, the only way that someone is brought into the kingdom of God is through repentance of sin and faith in the Lord Jesus Christ.