Sometimes we can mistake our familiarity with a term or phrase with our understanding of it. If you're not terribly sure what is meant by the Kingdom of God, then keep reading.
Did you know that the phrase, “Kingdom of God” occurs 122 times in the New Testament?
Did you know that 99 of these occurrences are found in the synoptic gospels (Matthew, Mark, and Luke)?
Did you know that 90 of those 99 occurrences come from the mouth of Jesus?
Yeah, me neither. That was until I read Jesus of Nazareth, volume 1 by, now, pope emeritus Benedict. If you haven't yet read it yet, you really should.
let's examine three historic and harmonizing interperetations of the kingdom of God, each of which shed light on this important concept.
The Christological Dimension
Here we see that “the Kingdom is not a thing, it is not a geographical dominion like worldly kingdoms. It is a person; it is he. On this interpretation, the term ‘Kingdom of God’ is itself a veiled Christology. By the way in which he speaks of the Kingdom of God, Jesus leads men to realize the overwhelming fact that in him God himself is present among them, that he is God’s presence.” (Pope Benedict, Jesus of Nazareth, Part 1)
The Idealistic/Mystical Dimension
Here we see that The Kingdom of God resides in the heart of man. Church Father, Origen  wrote, “those who pray for the coming of the Kingdom of God pray without any doubt for the Kingdom of God that they contain in themselves, and they pray that this kingdom might bear fruit and attain its fullness.”
The Ecclesiastical Dimension
Here we see that the kingdom of God is in the here and now, present in and through the Church. Yet it is a mixed reality that will only be perfectly realized at the end of history. This current “mixed” state can be seen as the Church on earth which now grows in the field of the world with both weeds and wheat until the harvest when Christ says he will “tell the reapers, Gather the weeds first and bind them in bundles to be burned. But gather the wheat into my barn” (Matt 13:30).
 I call Origen a Church Father because in his Wednesday catecheses on the Church Fathers which went from March, 2007, to June, 2008, Pope Benedict XVI devotes two talks to him; good enough for me.