"...Thy kingdom come on earth as it is in heaven.."
These words are from the Lord's prayer. Jesus is telling the disciples that they should pray for God's kingdom to come on earth. This is Christ's kingdom He is talking about. Christ became man in order to bring in His Kingdom. He told Pilate He was a king, but His kingdom was not of this world. So what is His Kingdom? This world in its present state is not God's kingdom. Such evil, malice, wickedness and cruelty can never be a part of God's kingdom. Jesus also said that the Kingdom of God is within you.
In a nutshell, it is God's plan to bring about His kingdom on earth through his subjects who have the Kingdom of God dwelling in them. We have the Kingdom of God dwelling in us when we have the King dwelling in us. If we let Him, He will live His life through us and we as obedient servants will do His work in this world. We are to be His ambassadors and representatives of the Kingdom. Those who dwell in this world will know what the Kingdom is like and who the King is when we His subjects are faithfully living like the King wants us to live. This is the way that the Kingdom will come on earth.We who have chosen Christ as King of our life are to be a part of bringing in the Kingdom by living Kingdom-like lives. No easy task -- and what a responsibility!