The concept of a threefold office in Christ was first of all taught by Calvin (1500s).
“Therefore, that faith may find in Christ a solid ground of salvation, and so rest in him, we must set out with this principle, that the office which he received from the Father consists of three parts. For he was appointed both Prophet, King, and Priest.”
Calvin saw the need to bring out these categories in order to rightly understand why Christ had been sent by the Father and what He had conferred upon His people. These areas of systematic theology focus on Jesus’ role as our Mediator.
The study of Jesus as Prophet, Priest, and King is often taught under two main other categories pertaining to Christ. The nature of this threefold office in His Humiliation, and the nature of this threefold office in His Exaltation.
The nature and necessity of the Mediator,
1 Timothy 2:5 5 For there is one God, and one mediator also between God and men, the man Christ Jesus,
Here Paul clearly calls Jesus a man, “the man” Christ Jesus. Yet in the fulfillment and execution of the various offices of Christ, it must be a requisite for Him to be more than a man. Thus, He is not just the “the man” “Jesus” but the man “Christ Jesus” i.e. the Divine Messiah who is also the man Jesus of Nazareth who can intercede on behalf of His people, who can reveal the mind of God to His people, and who can govern and rule over His people.
We could say that the entire presentation of Christ’s threefold office is bound up in His essential role as Mediator. As Mediator Jesus communicates God’s Word to God’s people through His prophetic office, as Mediator Jesus brings God’s people to Him through the sacrifice of His own life in His priestly service, and as Mediator Jesus brings God’s kingdom and rule to govern God’s people ruling over them as King of kings and Lord of lords. As the Mediator between God and man, Christ must be Prophet, Priest, and King.
Our practical need of Jesus as Prophet, Priest, and King
The threefold office of Christ is a virtual prism of Christology and has massive practical importance for us today. We should probably pause to contemplate the Old Testament roots of these offices and their redemptive inception. As Bavinck put it, “Already under the Old Testament [dispensation], he was active as prophet, priest, and king.” He was implied in the Fall, from a redemptive historical point of view, the fall demands His role as Mediator who is embedded in the promise (Gen. 3.15) and who will speak by His Spirit about our salvation through the prophets (1 Pet. 1.9-11). The OT is full of Jesus’ priestly duties. These are seen by the institutions of the earthly priesthood who do on earth what Jesus would do in heaven (Heb. 9.11-14). They are the type, He is the antitype. The OT is also full of Jesus’ kingly office. The kingship of Christ is embodied in the Davidic kingdom the way Jesus’ priesthood is embodied in Aaron’s priestly role (Heb. 5.4). What follows in the New Testament is refined Christology where His offices are no longer in shadow form, the types have been fulfilled and His role as Prophet, Priest and King executed to the glory of God and the good of His people (Heb. 2.17).
Practically, we have need of all of Jesus’ offices. Without Jesus’ prophethood, He does not deliver to us the final word of God (in His own ministry and saying and by extension in His holy apostles). But this is precisely what Hebrews tells us He did:
Hebrews 1:1–2 1 God, after He spoke long ago to the fathers in the prophets in many portions and in many ways, 2 in these last days has spoken to us in His Son, whom He appointed heir of all things, through whom also He made the world.
Jesus cannot be separated from the Word, He is the Word (John 1.1, 14). This means we do not need to be confused about what God wants, what God requires, and what God provides through Jesus Christ. We are not confused because, even though we live in a world of utter confusion, He prophesies to us concerning the truth (John 1.17). It is this truth that makes Him intolerable to the world (John 7.7).
As our Priest, Jesus is our High Priest (Heb. 4.15) and as our High Priest is the final Priest (Heb. 5.6), the perfect Priest who does all that is in Gods’ heart (1 Sam. 2.35). He is a permanent Priest who consequently creates in His people a kingdom of priests (Rev. 5.10). That Jesus makes us “priests” means that not only that Jesus represents us to God and God to us (cf. Ex. 28.2, 9-12); He we also justifies us so that as justified priests we can no come to God boldly, we can enter into God’s throne room, into the Holy Place through a new and living way we can draw near via His own blood (Heb. 4.16; 10.19-20) and consequently represent God to others through our evangelistic efforts (Rom. 15.16). The effects of Jesus’ priestly role in our lives is simply staggering.
Finally, as our King, He is the King of kings and Lord of lords. His kingship elicits our allegiance and adoration (cf. Ps. 2.11-12). In Jesus we know the friendship and the fear of knowing one who is so terrible in authority and wrath and yet so tender and compassionate as the highest King of all the earth (Ps. 89.27). Jesus’ kingship stems from what God has promised Him (Ps. 89.33-35). He has given Him the throne of His father David (Lk. 1.32). As consequence, the New Testament tells us that we are fellow heirs with Christ (Rom. 8.17), that we will reign with Him (2 Tim. 2.12), judge angels (1 Cor. 6.3) and sit on His throne (Rev. 3.21). As King, Jesus also rules over all of the affairs of man as totally sovereign (Ps. 2.10-12; Dan. 7.13-14) and no one will escape His Lordship (Phil. 2.9-11).
When we think about the birth of Jesus and the Christmas season, we recall that God called His Son into the world for a purpose. That purpose is really only fully understood as we contemplate Jesus as our Mediator and if our Mediator than Prophet, Priest, and King from which we cannot be separated. Christmas is about the advent of Christ; His offices remind us that He is forever with us. Heresy cannot separate us from our Prophet, sin cannot separate us from our Priest, and the politics of the present evil age cannot separate us from our King. This is why the Threefold Office of Christ matters and this is why He came.
 John Calvin, Institutes of the Christian Religion (Bellingham, WA: Logos Research Systems, Inc., 1997).
 Herman Bavinck, John Bolt, and John Vriend, Reformed Dogmatics: Sin and Salvation in Christ, vol. 3 (Grand Rapids, MI: Baker Academic, 2006), 365.