In Christianity, as in Judaism, all worship of God is through the High Priest. The only approach to God is through the High Priest and God’s acceptance of the High Priest assures acceptance of the people the High Priest represents. Under Judaism, for centuries the Israelites had looked to their high priest - descendant of Aaron – to represent them before God, now under Christianity, the Jews were to turn from this Aaronic priesthood to their great High Priest Jesus Christ, who did not descend from the priestly tribe of Levi. The writer now has to convince these Jewish believers that this Jesus was really superior to the Aaronic priests, and had actually superseded them. Christ is of the order of Melchizedek but exercises His office after the pattern of Aaron.
Continuing his discussion on the priesthood  from where he first mentioned the High Priest , the writer of the Epistle proceeds to introduce Melchizedek and to describe his origin and office. The first scriptural reference to Melchizedek is found in the book of Genesis . Here Melchizedek is described as: King of Salem (Jerusalem); Priest of God Most High; King of righteousness and peace (also a reference to Messiah Isa. 9:6-7) “Without father or mother, without genealogy, without beginning of days or end of life,” unlike other notable individuals, no mention of his genealogy is given in the record.
“..like the Son of God” [“Like” Strong’s Greek/Hebrew Dictionary: to assimilate closely: (assimilate = blend; conform; adapt;) make like: resemblance; similar; compare.] Personally, but not typically, he resembles the Son of God (N.T. for English Readers – Henry Alford), the description in verse 3 [“Without father or mother,] fully applies to Christ only in His Deity, not in His humanity. The writer, in outlining the attributes of Melchizedek, compares him to Christ and this is one of those difficult passages of Scripture that must be accepted simply and trustingly in the way it is presented, and wait for a full revelation on a coming day. There should be no conclusion that Melchizedek had no parents, or that he was never born, or died. The point is that his office as priest was not dependent upon these vital statistics.
“…….he remains a priest forever.” Jesus is our eternal High Priest and since Melchizedek has no genealogical record, his priesthood continues “like” that of Jesus; Melchizedek, therefore, is a picture of an eternal priesthood. The writer says that Melchizedek is “made like” the Son of God, not that the Son of God is like Melchizedek. Thus it is not that Melchizedek sets the pattern and Jesus follows it. Rather, the record about Melchizedek is so arranged so as to express certain truths that apply far more fully to Jesus than they do to Melchizedek. [Matthew Henry’s Commentary]
“Now the law requires the descendants of Levi who become priests to collect a tenth from the people”…. “This man, however, did not trace his descent from Levi”  Melchizedek preceded the Law of Moses and the Aaronic priesthood and collected the tithe and blessed Abraham, although Abraham possessed the promises of God. Here we see that the lesser person is blessed by the greater – “Just think how great he [Melchizedek] was” Aaron paid the tithes through Abram, making Melchizedek greater than Aaron.
JESUS – HIGH PRIEST FOREVER
“…why was there still need for another priest to come..”  The Levitical priesthood was imperfect and since all priests, from Aaron through his descendants, were limited in their service due to death, a better priesthood was necessary. The Law and the priesthood went together, and all the people, as sinners, were condemned by the Law (“for on the basis of it the law was given to the people”) Therefore a better priestly system was necessary to mediate between God and the people and He promised an eternal priesthood that would not be limited by the condemnation of the Law or the replacement of the priest due to death.
A change of the priesthood requires a change of the law:  The Law stated that all priests were to be selected from the tribe of Levi . The passage here is speaking about The Lord Jesus Christ who descended from the tribe of Judah but Moses, in the Law, made no mention of priests being selected from the tribe of Judah; therefore another priest like Melchizedek is appointed, not on the basis of the Law but on the basis of the power of an indestructible life. The former regulation of the Law is now set aside because of its weakness in not being able to make anything perfect and a better hope is introduced; unlike all the priests before Him who were ordained without an oath, Christ became high priest with an oath and the guarantee of a better covenant. 
“The Lord has sworn and will not change his mind: ‘You are a priest forever.”  Because Jesus lives forever His priesthood is permanent or eternal and He is fully acceptable by God as our High Priest because of His resurrection from the dead. God’s people will never more be without a priestly representative, His is able to save eternally, because He ever lives to intercede for sinners.
“Such a high priest meets our need”  He meets the need of our salvation and the consequence of sin but unlike the other high priests, He is set apart from sinners and does not need a daily sacrifice for His own sins and for the sins of the people (for He is sinless).  He offered one sacrifice for all times for the sins of His people in the offering of Himself. The oath, which came after the Law, appointed Jesus, God’s Son, as High Priest who is perfected forever.
“The LORD has sworn and will not change his mind: “You are a priest forever, in the order of Melchizedek.”