When we pray "Thy kingdom come", we are praying this in the sense that God will through us His Church, show the world a semblance of what His Kingdom will truly look like when Christ has come a second time to take over and rule over this world.
We are also asking God, to speed up the return of of His son Christ Jesus.
Again, when we pray " Thy will be done on earth as it is in heaven" we are asking as the church, that God by His guidance through Him the Holy Spirit, will have us pray along the lines of His will.
Jesus did say we are to love and worship the Lord your God with all your heart soul and strength, as well as to love your neighbor as yourself. If we pray along these lines as well as living our lives along these lines in other words letting these prayers inform how we live, then His will, will be done on earth