Quoted Scriptures are from the Contemporary English Version unless otherwise noted
To understand the Melchizedek priesthood, first we need to get a quick background of who Melchizedek was:
Genesis 14:17-18 introduces Melchizedek as the king of Salem (which later became Jerusalem) and priest of the Most High God, Yahweh. Genesis Chapter 14 tells of how Abram (who's name was changed later to Abraham, Genesis 17:3-5) had to go rescue certain family members from kidnappers. After successfully doing so, King Melchizedek came to Abram with bread and wine and proceeded to bless Abram. In return, Abram gave the king a tenth of his belongings. It is interesting to note that this priest of God is not someone of the Israelite genealogy, for the Abrahamic covenant hadn't even been made yet (that comes along later, in Genesis 15:18), nor had the Israelites themselves existed yet (they come into existence starting at Genesis 32:27-28).
MELCHIZEDEK AND CHRIST
Evidently, King/ Priest Melchizedek was a foreshadowing of Christ, for Hebrews 5:4-10 states:
4 But no one can have the honor of being a high priest simply by wanting to be one. Only God can choose a priest, and God is the one who chose Aaron. 5 That is how it was with Christ. He became a high priest, but not just because he wanted the honor of being one. It was God who told him, "You are my Son, because today I have become your Father!" 6 In another place, God says, "You are a priest forever just like Melchizedek." 7 God had the power to save Jesus from death. And while Jesus was on earth, he begged God with loud crying and tears to save him. He truly worshiped God, and God listened to his prayers. 8 Jesus is God's own Son, but still he had to suffer before he could learn what it really means to obey God. 9 Suffering made Jesus perfect, and now he can save forever all who obey him. 10 This is because God chose him to be a high priest like Melchizedek
The book of Hebrews further explains Christ's co-relation to Melchizedek at Hebrews 6:19 - 7:17 as shown point by point here:
19 This hope is like a firm and steady anchor for our souls. In fact, hope reaches behind the curtain and into the most holy place. 20 Jesus has gone there ahead of us, and he is our high priest forever, just like Melchizedek. (Psalm 110:4) 7:1 Melchizedek was both king of Salem (Matthew 21:1-5, John 12:12) and priest of God Most High (Hebrews 3:1, 8:1). He was the one who went out and gave Abraham his blessing, when Abraham returned from killing the kings. 2 Then Abraham gave him a tenth of everything he had. The meaning of the name Melchizedek is "King of Justice." (Acts 17:31) But since Salem means "peace," he is also "King of Peace." (Colossians 1:20, Revelation 19:11-20:3)3 We are not told that he had a father or mother or ancestors or beginning or end. He is like the Son of God and will be a priest forever. (John 1:1, 8:58, 17:5)
Now, notice the remainder of this passage:
4 Notice how great Melchizedek is! Our famous ancestor Abraham gave him a tenth of what he had taken from his enemies.
(For Melchizedek to receive tithes from Abraham was a big deal, for Abraham was a very prominent figure who was about to be covenanted to Yahweh)
5 The Law teaches that even Abraham's descendants must give a tenth of what they possess. And they are to give this to their own relatives, who are the descendants of Levi and are priests.
6 Although Melchizedek wasn't a descendant of Levi, Abraham gave him a tenth of what he had. Then Melchizedek blessed Abraham, who had been given God's promise.
7 Everyone agrees that a person who gives a blessing is greater than the one who receives the blessing.
(Remember, Melchizedek blessed Abram).
8 Priests are given a tenth of what people earn. But all priests die, except Melchizedek, and the Scriptures teach that he is alive.
9 Levi's descendants are now the ones who receive a tenth from people. We could even say that when Abraham gave Melchizedek a tenth, Levi also gave him a tenth.
10 This is because Levi was born later into the family of Abraham, who gave a tenth to Melchizedek.
11 Even though the Law of Moses says that the priests must be descendants of Levi, those priests cannot make anyone perfect. So there needs to be a priest like Melchizedek, rather than one from the priestly family of Aaron.
(The Aaronic priesthood of the nation of Israel was through the Levites Numbers 26:59, Exodus 28:40-41 , whereas Melchizedek has no Israelite ties at all, thus a difference in priesthoods)
12 And when the rules for selecting a priest are changed, the Law must also be changed.
(because the covenant was being replaced 2 Corinthians 3:14)
13 The person we are talking about is our Lord, who came from a tribe that had never had anyone to serve as a priest at the altar.
14 Everyone knows he came from the tribe of Judah, and Moses never said that priests would come from that tribe.
(Christ's earthly life descended from Judah, not Levi Matthew 1:1-16 , thus Christ was not of the Old Covenant priestly class of Levites, therefore making him the priest is creating a change of the priesthood)
15 All of this becomes clearer, when someone who is like Melchizedek is appointed to be a priest.
16 That person wasn't appointed because of his ancestors, but because his life can never end.
17 The Scriptures say about him, "You are a priest forever, just like Melchizedek."
OTHER MEMBERS OF THE PRIESTHOOD
Now, does this mean that Christ is the only member of the Melchizedek priesthood? No, for the Bible clearly states God will choose others to join Christ as priests in the heavenly kingdom:
"You let them become kings and serve God as priests, and they will rule on earth."
May kindness and peace be yours from Jesus Christ, the faithful witness. Jesus was the first to conquer death, and he is the ruler of all earthly kings. Christ loves us, and by his blood he set us free from our sins. He lets us rule as kings and serve God his Father as priests. To him be glory and power forever and ever! Amen.
These people are the first to be raised to life, and they are especially blessed and holy. The second death has no power over them. They will be priests for God and Christ and will rule with them for a thousand years. No other dead people were raised to life until a thousand years later.
This all fits together neatly, for Christ is the priest from the tribe of Judah, and it is Judah who will be ruling over Israel.(For more information regarding spiritual Judah and spiritual Israel click here)
Looking at this information, it is quite plain that the Aaronic priesthood was replaced with the Melchizedek priesthood when God replaced the Old Covenant with the New Covenant. It is also quite plain that Christ is the high priest of this priesthood and others will join him in the priestly duties for at least one thousand years. Therefore, those who are chosen to be a part of the Melchizedek priesthood will be those chosen to rule with Christ.