What does it mean to say that the Kingdom of God is "right now, but not yet"?

To say that the Kingdom of God is "right now, but not yet" means that Jesus always gave all of himself to God. By "selling all that we have", but not literally, we can fully find ourselves in the presence of God's reign.

When discussing Jesus' teachings, what is a better reference for the word kingdom?

When discussing Jesus' teachings (Kingdom), a better reference is Reign of God.