The Kingdom of God is something that can be entered into. But only those who are "born again" can enter into it. We who are born of the flesh are flesh—just mortal flesh and blood. We were born that way. But it is possible for us to be born again—this time not as a mortal, flesh-and-blood baby, but born of the very Spirit of God. Then we shall be spirit—wholly composed of spirit as God is (John 4:24)!
God is not a single Personage. The Hebrew word for God, elohim, denotes more than one person. It shows God is a single Family, or "Kingdom," but composed of more than one person.
We have the mineral kingdom, the plant kingdom, and the animal kingdom. The Bible reveals an angel kingdom, created by God and composed of spirit. And then, high above all is the very creating kingdom—the God Kingdom. In other words, the "Kingdom of God"! God the Father and Christ the Son presently compose the Kingdom or Family of God.
The astounding truth of the Bible is that God is reproducing Himself! God created mortal man in God's own image so that we may become impregnated—begotten—by the Spirit of God. Then, by a resurrection (I Corinthians 15:50), we may be born of God—"born again"—as immortal, spirit-composed persons in the Kingdom or Family of God!
