The origin and purpose of the Hebrew priesthood is described in Hebrew 5:1-10.
The priest is taken from the people and ordained for the people. The first step of Jesus toward acquiring his priestly office was to become a member of the human race. Following that he offered his most precious sacrifice for the people. The very nature of a priest is one who offers sacrifices and intercessory prayers to God.
By nature Jesus was totally spiritual; human qualities were added later. We, by nature, are human and we strive to become spiritual. The Lord, by being both human and divine, became the perfect mediator between God and people. Jesus is also the victim; offered up by himself—of his own free will. These deeds of Jesus, took place “in the days when he was in the flesh.”
These are the days we are now in the flesh. We can join our sacrifices and intercessions this very day, with the sacrifices of Jesus. Daily we can live spiritually by offering our gifts, our time and especially our suffering to the Father, in union with Jesus the priest.