Short answers, pulled from the story.
The threefold office, known in Latin as the munus triplex, is the Christian doctrine that Jesus Christ performed three functions in his earthly ministry: those of prophet, priest, and king. The doctrine holds that all other roles attributed to Christ fall under one of these three distinctions.
Eusebius first worked out the threefold classification, describing Jesus as the only high priest, the only King of every creature, and the supreme prophet of prophets. The doctrine was more fully developed by John Calvin, who completed his presentation of all three offices in the third edition of his Institutes of the Christian Religion in 1559.
In Lord's Day 12, Question and Answer 31, the Heidelberg Catechism explains that Jesus is called Christ, meaning "anointed", because he was ordained by God the Father and anointed with the Holy Spirit to serve as chief prophet and teacher, only high priest, and eternal king. The catechism ties the title directly to all three offices.
According to the doctrine of the threefold office, Jesus never used the prophetic messenger formula because he is identified as the Logos, the source of revelation itself, rather than a channel passing along someone else's words. Old Testament prophets spoke for God; the doctrine holds that Jesus spoke as the Word of God.
Old Testament priests repeatedly offered animal sacrifices on behalf of the people, but Christ offered himself once as the atoning sacrifice. The Book of Hebrews, particularly chapters 7 through 10, argues that Jesus holds the priestly office with an indestructible power, unlike the mortal weakness of human priests, and makes continual intercession before God.
The Catechism of the Catholic Church states that Jesus fulfilled the messianic hope of Israel in his threefold office of priest, prophet, and king. The Second Vatican Council's Decree on the Apostolate of the Laity extended the concept to all baptized people, affirming that lay persons share in the role of Christ as priest, prophet, and king.