Moses, the great prophet anticipated a greater prophet (Deuteronomy 18 v15). Jesus did do what prophets do: Deliver God’s message to God’s people. Not only did He deliver the message, He is the message; He is the Word of God (John 1 v1).
Jesus is also our High Priest, like Aaron and his sons initially were. Jesus did what priests do: represent God’s people in God’s presence by bringing their sacrifices and offerings. Not only did He bring the sacrifice, He is the sacrifice (Hebrews 7 v27).
As a descendant of David, Jesus was qualified to be King on David’s throne. Isaiah prophesied that the Messiah would be a King (Isaiah 9 v7). Jesus acknowledged to Pilate that He was indeed King of the Jews, as the crowds at His triumphant entry to Jerusalem recognised. When Jesus returns, He will reign on Earth (Revelation 17 v14; 19 v16) in fulfillment of David’s covenant, which promised David an eternal throne (2 Samuel 7 v16).
Condensed from Understanding Theology by Daryl Aaron.