This concept (the eternal nature of the priesthood) is also found in Hebrews. The way it was used by Paul has caused a great deal of confusion. Paul spoke of the priesthood as being without father, without mother, without descent, having neither beginning of days nor end of life (Heb 7:3). Yet this phrase, for centuries has been interpreted incorrectly to refer to the great High Priest, Melchizedek. Nobody was able to figure out how Melchizedek could have been born without father or mother, etc. The confusion is solved by latter-day revelation which makes it clear that the phrase has reference to the priesthood not Melchizedek.
Joseph Smith
"The Priesthood is an everlasting principle, and existed with God from eternity, and will to eternity, without beginning of days or end of years. The keys have to be brought from heaven whenever the Gospel is sent. When they are revealed from heaven, it is by Adam's authority." (Teachings, p. 157)