Question: Since, then, you say that the additional name “Christ” or “Anointed” implies that He came with the command of the Father to establish a royal priesthood, explain first what the kingdom of Christ is.
Answer: A kingdom is a kind of rule over a people in which one person serves as the head and is exceptionally gifted with wisdom, counsel, and strength, so that his subjects benefit from his wisdom and other gifts and live happily and peacefully under such a head.
This helps us to understand what the Kingdom of Christ is: it is a kind of rule over the people of God in which there is one head, namely, Christ the Lord, who is gifted far beyond all angels and people with wisdom, counsel, might, and all other gifts. This head, Christ, rules His subjects even in this life in such a way that He produces eternal salvation in the hearts of all the elect through the preaching of His holy gospel and the power of His Spirit.
He does this by incorporating them into Himself by faith and the testimony of holy baptism, by graciously not imputing their sins to them, by daily purifying them from sin, by living in them and ruling their hearts with His Holy Spirit, and by using as means to that end the preaching of the holy gospel, the administration of the holy sacraments, and Christian discipline. This is in order that in this life they might live happily in the Lord, have peace with God, and at last in eternity live and reign with their King. This is the Kingdom of Christ that begins in this life and will increase in the heart of every believer (John 15; Matthew 25; Mark 1).
Caspar Olevianus, A Firm Foundation, p. 37