"And it was this same Melchizedek to whom Abraham paid tithes; yea, even our father Abraham paid tithes of one-tenth part of all he possessed."
I've already commented that I believe Melchizedek (whose name means "king and priest") was in fact Shem. I believe those who disagree (McConkie and Joseph Fielding Smith) base their conclusion on the words of D&C 84: "Which Abraham received the priesthood from Melchizedek, who received it through the lineage of his fathers, even till Noah;" (D&C 84: 14). I believe the lineage referred to there is from the fathers who preceded Noah. But Noah was Shem/Melchizedek's father.
Abraham received the priesthood which had been promised to him by God, from Melchizedek. He (Abraham) already had the records of the fathers. (Abr. 1: 31.) He already had the promise of priestly authority. (Abr. 2: 6-9.) So the question should be asked as to why Abraham would need to be ordained by Melchizedek when the Lord was speaking directly to him and could have taken care of that directly. It is an important question. It is necessary to understand why the question should be asked and also what the answer is.
First, why would Abraham, who was directly in contact with God, be sent to another to receive the priesthood? What sense does it make the Lord would make him wait and send him to another? Particularly when Abraham had understanding that stretched into heavens and also possessed the records of the fathers, back to Adam. Why do that?
You should struggle with this question yourself. I feel like I'm robbing you by answering. Nevertheless, Abraham needed to be endowed and Melchizedek was set up to provide to Abraham the endowment. Therefore to receive the ordinance (Abraham was raised by apostates who had not provided that for him), he was sent to Melchizedek from whom he received necessary ordinances. As long as the ordinances needed to be performed and there was an officiator there to accomplish it, the Lord sent Abraham to Melchizedek.
Abraham also received the accouterments of kingship that descended from Adam. Melchizedek was the reigning high priest on the earth, Abraham was to replace him at his passing, and Melchizedek had awaited the promised successor's arrival for years. When at last Abraham arrived, Melchizedek was able to provide ordinances, answer questions, minister as was needed, then turn over the accouterments of kingship and withdraw from this earth. No sooner had Abraham been prepared than Melchizedek and his city also withdraw to join Enoch's people.
Second, why were tithes paid to a great high priest who would shortly be translated? What need was there for tithing?
The form the tithing took was not a check or bank draft. It was animals, food and usable material. What was provided would be used in sacrifices, feasts, celebrations and decoration of the temple maintained by Melchizedek. In short, Abraham provided material through his tithing that could be incorporated into the celebrations to which he was invited and from which he derived his own blessing and endowment. He gave, in turn he received.
Now, if you do not understand the concept of meekness and its importance for one who should hold this holy priesthood, then you do not understand either Melchizedek or Abraham. Each was a minister who served others. Each was a faithful guide because neither sought to be greater than another. They were great servants, who could be trusted with great authority because they did not seek their own will. They were interested in following the Lord's will. Even at the price of great inconvenience and sacrifice to them. They were willing to sacrifice all things, and were therefore called to the work.