The word "kingdom" means "the realm over which a king rules." When applied to God, it could refer to all creation, since "his kingdom ruleth over all" (Psalm 103:19), but the kingdom more often applies to His rule in and through those who are submitted to Him. "The Kingdom of God" more specifically refers to Christ living and ruling in our hearts. Praying "thy kingdom come" is praying for the expansion and influence of God's rule in the hearts of men everywhere and, the establishment of His physical Kingdom here on earth at His second coming (Revelation 11:15; 20:4).

Throughout Jesus' earthly ministry, the Jews kept looking for Jesus to establish a physical kingdom here on the earth and deliver them from the oppression of the Romans.  During the Millenium, the Kingdom of God will physically rule over the nations of the earth. Jesus' Kingdom is spiritually established by His Word and not by carnal weapons (2 Corinthians 10:3-5). Jesus said, "The Kingdom of God cometh not with observation . . .behold, the kingdom of God is within you." (Luke 17:20-21). Paul says we are already in the Kingdom of God (Colossians 1:13). The Kingdom of God is therefore Christ's "invisible Church," His body. The Kingdom began during His earthly ministry and is still ruling the hearts of men.

The new birth takes us into the Kingdom of God which is infinitely greater in wonder and benefits than our finite minds can comprehend. To the degree that we do begin to understand how God's Kingdom works and apply our lives to it, we can experience heaven here on earth. We can pray for a release into the physical of what is already present in our spiritual being.