The word priesthood has two meanings. First, priesthood is the power and authority of God. It has always existed and will continue to exist without end (see Alma 13:7–8; D&C 84:17–18). Through the priesthood, God created and governs the heavens and the earth. Through this power, He exalts His obedient children, bringing to pass “the immortality and eternal life of man” (Moses 1:39; see also D&C 84:35–38).
Second, in mortality, priesthood is the power and authority that God gives to man to act in all things necessary for the salvation of God’s children. The blessings of the priesthood are available to all who receive the gospel. (“Priesthood Authority” Handbook 2, Administering the Church)
In the spring of 1835, Joseph Smith received a revelation explaining the name of the priesthood: “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. All other authorities or offices in the church are appendages to this priesthood. … The second priesthood is called the Priesthood of Aaron, because it was conferred upon Aaron and his seed, throughout all their generations. Why it is called the lesser priesthood is because it is an appendage to the greater, or the Melchizedek Priesthood, and has power in administering outward ordinances” (D&C 107:1-5, 13-14).