The word Kingdom is made up of two words: "King's Domain' (or King-dom). It is the territory, or area, over which a King rules and reigns. God's Kingdom is the reign and rule of God, whether in heaven or earth.
In the New Testament, the Kingdom of God is more than a territory that belongs to God; it is also God's Sovereignty. That is, His quality, or state of being; His status, power, and authority. Because of His Sovereignty, His Kingdom is more than territory, and it speaks of a state and condition of things in which God rules and reigns supreme.
The New Testament word for kingdom is the Greek word 'basileia'. It means the sway, rule, and administration of a King. The King and Kingdom cannot be separated as a New Testament concept. The word Kingdom is used 160 times in the New Testament. The Kingdom of God, and the Kingdom of Heaven are basically the same thing, and are generally interchangeable in Scripture.
The idea of the Kingdom of God, and the Sovereignty of God was a concept that was central to the message of Jesus. The announcement of His Kingdom was the major element of His teaching. He wanted to rule and reign the people of the whole earth, and not just the people of Israel. The Kingdom is to bring the Heavenly Father's government to all people. His government is Righteousness and Justice for all people in His Kingdom. God, the Father, wants all people to come under the Kingship of Jesus Christ.
The way for all people to come into the Kingdom is by Repentance. Each person must repent, or turn away from sin, and receive the King. The coming of the Kingdom into this world is a new (and literally) earth shaking situation. The emergence of this Kingdom has put everything that has gone before out of date. This is a new covenant lived in a new perspective, that is, the Kingdom of God.
The Kingdom of God is a present reality. Jesus said, "The Kingdom is within (among) you".1 It is literally within us. Because the Kingdom is within us, we must respond Internally. It is a remaking of the heart of people by living with the Kingdom standards of the Beatitudes of Matthew 5:3-12.2 The work of the new Kingdom in us is to produce a new heart and mind. This process of remaking people from the inside out (not the outside in) is the work of the Holy Spirit of God.
The Kingdom of God is freely given to anyone who will ask for the King, Jesus. If we have the King then we have His Kingdom. Though it is free, Jesus makes it very clear that we should do whatever is necessary to get the Kingdom. We must have a child-like spirit, a forgiving spirit, a heart of love, a standard of righteousness, and a pure heart. We must not have such a deep tie to the world, power, position, or anything else that might hinder or make difficult our entrance and acceptance of the Kingdom of God.
The Kingdom of God is defined this way: The Kingdom is a state of things on earth in which God's will is as perfectly done as it is in Heaven.3
1. Luke 17:21
2. Matthew 5:3-12
3. Matthew 6:10