Melchizedek, without father, without mother, without descendant, having neither beginning of days nor end of life, king of righteousness, king of peace (Salem), priest of the Most High God, a superb type of Christ.
As usual, I like Pink on this. 'From Gleanings in Genesis' by A.W. Pink:
http://www.pbministries.org/books/pink/Gleanings_Genesis/genesis_19.htm
Some have thought he was
Shem who was a contemporary of Abram’s for a hundred years;
but this cannot be, for we are distinctly informed concerning Melchizedek that
he was "without father, without mother" (Heb. 7:3), which, as we shall see, means that Scripture is absolutely silent concerning his genealogy.
This then disposes of the Shem theory, for we do know who his father was. Others have concluded that he was
Christ Himself, but this supposition is equally unscriptural for we are told that
Melchizedek is "made like unto the Son of God" and that Christ’s priesthood is "after the similitude of Melchizedek" (Heb. 7:3, 15), which could not be said if Melchizedek were Christ Himself. Still others have supposed that he was some
mysterious celestial being, but that is emphatically negatived by
Hebrews 7:4, where
Melchizedek is expressly called a "man."
In the words "made like unto the Son of God" (Heb. 7:3) we have the key to the mystery which centers around Melchizedek.
Melchizedek was a type of Christ, and particularly a type of our Lord’s priesthood. There are other points of resemblance which we shall consider below, but the first point of analogy between Melchizedek and the Son of God singled out by the Holy Spirit in Hebrews 7 is that he is
"without father, without mother, without descendant, having neither beginning of days nor end of life." This does not mean that Melehizedek was a supernatural, a divine being, but that he is presented to us in the Old Testament as without father or mother, etc. In other words, the silence of the Old Testament Scriptures concerning his parentage has a designed significance.
The entire omission of any reference to Melchizedek’s ancestry, birth or death, was ordered by the Holy Spirit (who "moved" Moses both in what he inserted and what he left out of the Genesis narrative) in order to present a perfect type of the Lord Jesus. No information concerning the genealogy of Melchizedek is recorded in Genesis, which is a book that abounds in genealogies. This is an instance where speech is silvern and silence golden. The silence was in order that there might be a nearer approximation between the type and the glorious antitype.
Not only was Melehizedek a type of our Lord in the fact that he is presented to us in Genesis as being "without father, without mother," but also in a number of other important particulars.
Melchizedek was a priest—"the priest of the Most High God" (Gen. 14:18). But not only so,
he was a king—"King of Salem "—and therefore
a royal priest. In the person of Melchizedek the offices of priest and king were combined, and thus was he a notable type of our great High Priest who according to the flesh was not of the tribe of Levi, but of the tribe of Judah, the royal tribe (see Heb. 7:14). Not only was Melchizedek a type of the royal priesthood of Christ by virtue of his office as
King of Salem (which means "peace") but his name also had a typical significance.
"Melehizedek" means "king of righteousness." Here again there is a wonderful and blessed bringing together of things which out of Christ are divorced. Not only did Melchizedek combine in his person the offices of king and priest, but in his titles he united righteousness and peace.
Melchizedek was both king of righteousness and king of peace and thus did he foreshadow the blessed result of the cross work of our adorable Lord, for it was at the Cross that
"mercy and truth met together, and righteousness and peace kissed each other" (Ps. 85:10).