According to McConkie and Millet, the “holiest order of God” is the Melchizedek Priesthood (see D&C 84:18-19). Before the day of Melchizedek, this priesthood was called “the Holy Priesthood, after the Order of the Son of God” (D&C 107:3). Melchizedek, we are told, “having been approved of God, … was ordained an high priest after the order of the covenant which God made with Enoch, it being after the order of the Son of God; which order came, not by man, nor the will of man; neither by father nor mother; neither by beginning of days nor end of years; but of God; and it was delivered unto men by the calling of his own voice, according to his own will, unto as many as believed on his name” (JST, Genesis 14:27-29; italics added).
It is marvelously significant that the word order constitutes part of the proper name of the priesthood. The Lord’s house is a house of order, and all that is done in it must be done in proper and orderly fashion. Such words as ordain and ordinance, which are associated with the governing of the Church, are rooted in the word order. The holy order of God is the priesthood. It is the priesthood received by the young elder, the priesthood associated with the new and everlasting covenant of marriage, and the fulness of priesthood bestowed upon those ordained kings and priests of the Most High God (see Teachings, p. 322). [Joseph F. McConkie and Robert L. Millet, Doctrinal Commentary on the Book of Mormon, Vol. III, pp. 39-40]