In Genesis 14 there is a man named Melchizedek. He is not mentioned very much and you might argue that he does not seem very important from this text alone.
17 After Abram returned from defeating Kedorlaomer and the kings allied with him, the king of Sodom came out to meet him in the Valley of Shaveh (that is, the King’s Valley). 18 Then Melchizedek king of Salem brought out bread and wine. He was priest of God Most High, 19 and he blessed Abram, saying, "Blessed be Abram by God Most High, Creator of heaven and earth. 20And praise be to God Most High, who delivered your enemies into your hand." Then Abram gave him a tenth of everything.
(Genesis 14:17-20, NIV)
Except one of the Psalms, this is only one place in the Hebrew Bible where he is mentioned at all.
The Lord has sworn and will not change his mind: "You are a priest forever, in the order of Melchizedek."
(Psalm 110:4, NIV)
In the Christian New testament he is, however, mentioned in the book of Hebrews a lot—and it seems like he is really important there. The author of Hebrews makes an argument that spans from chapter 5 to chapter 7 were Christ is compared to Melchizedek:
5 In the same way, Christ did not take on himself the glory of becoming a high priest. But God said to him, "You are my Son; today I have become your Father.” 6 And he says in another place, "You are a priest forever, in the order of Melchizedek."
(Hebrews 5:5-6, NIV)
Christ is said to be indirectly "in the order of Melchizedek" in Hebrews 7:
7If perfection could have been attained through the Levitical priesthood—and indeed the law given to the people established that priesthood—why was there still need for another priest to come, one in the order of Melchizedek, not in the order of Aaron?
(Hebrews 7:11, NIV, emphasis mine)
Why is Melchizedek such an important character for the author of Hebrews and what does it mean that Christ is "in the order of Melchizedek"?
Please note: This question originally contained two different questions. The second has since been asked as a stand alone question.