Genesis 14:18-20: "Blessed be Abram by God Most High, Creator of heaven and earth ..."

Then Melchizedek king of Salem brought out bread and wine. He was priest of God Most High, "Blessed be Abram by God Most High, Creator of heaven and earth. And praise be to God Most High, who delivered your enemies into your hand." Then Abram gave him a tenth of everything. (Genesis 14:18-20)

Who was Melchizedek?

We find a clear statement in this verse about the Priest Melchizedek.

We also find that Melchizedek is described as being "priest of God Most High." This indicates that Melchizedek was considered a representative of God. A Prophet.

Melchizedek also "blessed" Abraham, and Abraham responded by giving the priest a tenth of his possessions.

This indicates that Melchizedek was Abraham's spiritual teacher.

To receive a blessing from a priest, and then to turn and commit what is now termed a tithing - and a significant one at that - indicates clearly that Abraham received instruction from Melchizedek.

We also find elsewhere clear evidence of Melchizedek's standing as a spiritual teacher, and a founding teaching in a spiritual lineage followed throughout the Bible:
The LORD has sworn and will not change his mind: “You are a priest forever, in the order of Melchizedek.” (Psalms 110:4)

And he says in another place, “You are a priest forever, in the order of Melchizedek.” (Hebrews 5:10)

We have this hope as an anchor for the soul, firm and secure. It enters the inner sanctuary behind the curtain, where our forerunner, Jesus, has entered on our behalf. He has become a high priest forever, in the order of Melchizedek. (Hebrews 6:20)
So we find that according to Hebrews, Jesus was also a teacher within this lineage, as was John the Baptist, Solomon, David, Samuel, Eli, Caleb, Joshua, Moses, Joseph, Jacob, Isaac and Abraham.

Is this a family lineage?

Within this lineage, we find clear evidence that this is not about ancestry. Melchizedek was clearly not related to Abraham. Samuel was not related to Eli. David was not related to Samuel. Caleb was not related to Joshua and Joshua was not related to Moses. And Jesus was not the son of John the Baptist, just as Peter was not the son of Jesus. Yet Peter continued the teachings of Jesus just as Jesus continued the teachings of Abraham, David and John.

And yes, some of these teachers may have been related to their students. Isaac and Jacob were possibly within the ancestry of Abraham, for example. But this is only if we accept that all instances of the Hebrew word, בֵּן (ben) have to mean "son." Contrary to this, the Hebrew word can also mean, "a member of a guild, order, class" - basically a follower or student.

Indeed, some translations of the Hebrews do indicate that this Hebrew word also describes students or followers.

What is the "blessing" Melchizedek gave?

The Hebrew word being translated into the word "blessed" here is בָּרַךְ (barak). This can mean "to bless," but also, according to Gesenius's lexicon, "Once used of the consecration of a sacrifice."

Jesus illustrated the process begun between Melchizedek and Abraham. Just as Melchizedek blessed Abraham, Abraham blessed Isaac (Genesis 25:11), Isaac blessed Jacob (Genesis 28:1), Jacob blessed Pharaoh (Genesis 47:10), Jacob blessed Joseph (Genesis 48:15) and his 11 other students (which each became lineages or "tribes") (Genesis 49:28), Moses blessed his followers, many who became priests, such as Joshua (Exodus 39:43), Joshua blessed Caleb (Joseph 14:13), Eli blessed Elkanah (1 Samuel 2:20), Samuel was later instructed by Eli, and Saul, who was Samuel's student, blessed David (1 Samuel 26:25). We find these types of blessings continued, sometimes referred to as "anointing."

And in the New Testament, we find that the blessings came in the form of baptism. We find that Jesus was baptized (blessed) by John, and Peter and his fellow disciples were baptized (blessed) by Jesus.

Thus we find that the "blessing" referred to between teacher and student throughout the Bible point to the acceptance of the student by the teacher, and the acceptance of the teacher by the student.

This is confirmed by the fact that Abraham gave Melchizedek a considerable tithing.

This is also confirmed by the various sacrifices and offerings that others who were "blessed" gave their teachers.

Such a "blessing" - the acceptance between teacher and student, is illustrated in the Book of Matthew:
Simon Peter answered, "You are the Messiah, the Son of the living God." Jesus replied, "Blessed are you, Simon son of Jonah, for this was not revealed to you by flesh and blood, but by my Father in heaven." (Matthew 16:16-17 NIV)

[From the Lost Gospels of Jesus:
And Simon Peter replied, saying, “You are the Anointed of God [Messiah, Christ], Representative of the living God. And Jesus responded, saying “Blessed are you, Simon son of Jonah: Because flesh and blood has not revealed this to you – but my LORD from the spiritual realm. (Matthew 16:16-17)]

Consider another translation of this verse in Chapter 14 of the New Book of Genesis.