As God is eternal, so also are all His works. They are without beginning of days or end of years, they having been prepared from everlasting to everlasting. The High Priesthood of God, by which He rules all things both in Heaven and upon the Earth, is eternal. It cannot and will not end. This High Priesthood, which is God’s Holy Order, was conferred upon good and righteous men; some were made Elders, some Seventies, and others High Priests. As God, himself, is a High Priest worlds without end, the High Priests so ordained were thereafter High Priests forever.
There are, in the Church, two Priesthoods, namely, the Melchizedek and Aaronic, including the Levitical Priesthood.
Why the first is called the Melchizedek Priesthood is because Melchizedek was such a great High Priest.
Before his day it was called the Holy Priesthood, after the Order of the Son of God
But out of respect or reverence to the Name of the Supreme Being, to avoid the too frequent repetition of His name, they, the Church, in ancient days, called that Priesthood after Melchizedek, or the Melchizedek Priesthood. (Doctrine and Covenants 107:1-4.)
And the sons of Moses, 1 according to the Holy Priesthood which he received under the hand of his father-in-law, Jethro;
And Jethro received it under the hand of Caleb;
And Caleb received it under the hand of Elihu;
And Elihu under the hand of Jeremy;
And Jeremy under the hand of Gad;
And Gad under the hand of Esaias;
And Esaias received it under the hand of God.
Esaias also lived in the days of Abraham, and was blessed of him—
Which Abraham received the Priesthood from Melchizedek, who received it through the lineage of his fathers, even till Noah;
And from Noah till Enoch, through the lineage of their fathers;
And from Enoch to Abel, who was slain by the conspiracy of his brother, who received the Priesthood by the commandments of God, by the hand of his father Adam, who was the first man—
Which Priesthood continueth in the Church of God in all generations, and is without beginning of days or end of years.
And the Lord confirmed a Priesthood also upon Aaron and his seed, throughout all their generations, which Priesthood also continueth and abideth forever with the Priesthood which is after the holiest Order of God.
And this greater Priesthood administereth the Gospel and holdeth the Key of the Mysteries of the Kingdom, even the Key of the knowledge of God. (Doctrine and Covenants 84:6-19)
And the Lord ordained Noah after His own Order, and commanded him that he should go forth and declare His Gospel unto the children of men, even as it was given unto Enoch. (Pearl of Great Price, Moses 8:19.)
And, finding there was greater happiness and peace and rest for me, I sought the blessings of the fathers, and the right whereunto I should be ordained to administer the same; having been myself a follower of righteousness, desiring also to be one who possessed great knowledge, and to be a greater follower of righteousness, and to possess a greater knowledge, and to be a father of many nations, a prince of peace, and desiring to receive instructions, and to keep the commandments of God, I became a rightful heir, a High Priest, holding the right belonging to the fathers.
It was conferred upon me from the fathers; it came down from the fathers, from the beginning of time, yea, even from the beginning or before the foundations of the Earth to the present time, even the right of the firstborn, on the first man, who is Adam, our first father, through the fathers unto me. (Ibid., The Book of Abraham 1:2-3)
Alma not only pointed to the calling of High Priests, but he also noted that men were ordained to that Priesthood by a holy ordinance. We do not know just what that holy ordinance was, but the Laying on of Hands by which the Priesthood of God is conferred and office in that Priesthood is given is a Holy Ordinance which is upheld by the Church of Jesus Christ of Latter-day Saints. How different from any self-appointed calling practised in many of the churches of the world today is the endowment of the Priesthood by this Holy Ordinance.
The purpose for which High Priests were ordained, or the duty that devolves upon one who has the Priesthood conferred upon him, is to preach God’s Holy Word, and also to teach others less enlightened than he, Heaven’s exalted Plans concerning his Salvation, that “he also might enter into the rest of the Lord.”