Hebrews 6:19-20

Since Jesus is our high priest forever, in the order of Melchizedek, it only makes sense to find out who Melchizedek is. With a quick search on BibleGateway.net, you find out that Melchizedek is mentioned first in Genesis 14:18-20:

Then Melchizedek king of Salem brought out bread and wine. He was priest of God Most High, and he blessed Abram, saying,
       "Blessed be Abram by God Most High,
       Creator of heaven and earth.

       And blessed be God Most High,
       who delivered your enemies into your hand."
      Then Abram gave him a tenth of everything. 

You see that Melchizedek, or King of Righteousness, Blessed Abram (later Abraham) and God Most High (El Elyon). You also see that Abram gave him a tenth of everything. You could say that Abram gave Mechizedek his tithe. Since Abram gave him a tithe, is understood that Melchizedek was superior to Abram. Given that he's superior, it stands to reason that the priesthood of Melchizedek is superior to the Aaronic priesthood, which came through Abraham.

Hebrews 7:10-12

10because when Melchizedek met Abraham, Levi was still in the body of his ancestor.

Jesus Like Melchizedek

 11If perfection could have been attained through the Levitical priesthood (for on the basis of it the law was given to the people), why was there still need for another priest to come—one in the order of Melchizedek, not in the order of Aaron? 12For when there is a change of the priesthood, there must also be a change of the law.