"And without doubt the lesser person is blessed by the greater. In the one case, the tenth is collected by men who die; but in the other case, by him who is declared to be living. One might even say that Levi, who collects the tenth, paid the tenth through Abraham, because when Melchizedek met Abraham, Levi was still in the body of his ancestor." NIV translation
Here, we see the ultimate in paying it forward as Paul describes the fact that Levi (servants of God) paid the tithe to Melchizedek as he was an ancestor of Abraham. Melchizedek's priesthood is compared to the Aaronic priesthood in that they were mere men that collected the tithe and, as men, they died but Melchizedek did not. Their ministry was temporary where Melchizedek's is permanent. We often forget that whatever ministry God has entrusted to us is, like Levi's, only temporary but it is for the eternal kingdom and has lasting effects.
"If 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?" NIV translation
Paul now contrasts the priesthood of Melchizedek with that of the Levites. We see that the law was administered by the Levitical priests and we know that the Law did not have the power to save men from their sins.
"For when there is a change of the priesthood, there must also be a change of the law." NIV translation
Before the Law of Moses was given, there was the priesthood of Melchizedek. With the giving of the Law, the Levitical priesthood was established. With Jesus our High Priest, we are under the law of love and not the Law of Moses.
"He of whom these things are said belonged to a different tribe, and no one from that tribe has ever served at the altar. For it is clear that our Lord descended from Judah, and in regard to that tribe Moses said nothing about priests. And what we have said is even more clear if another priest like Melchizedek appears, one who has become a priest not on the basis of a regulation as to his ancestry but on the basis of the power of an indestructible life. For it is declared: 'You are a priest forever, in the order of Melchizedek.'" NIV translation
Now, Paul begins to compare Jesus (our High Priest) to the Levites. Jesus was from the tribe of Judah and they were not the tribe that was set aside to be priests by the Law of Moses. He was declared a priest by His resurrection as it is said in Psalm 110:4. This is also the basis for the doctrine commonly called "the doctrine of the priesthood of all believers".
In 1 Peter 2:5, Peter speaks of the fact that we become priests based on our relationship with Jesus Christ. As Jesus' priesthood was confirmed by the power demonstrated in His resurrection, our priesthood is confirmed by the power of the Holy Spirit that works in and through us.
Today, their has been a religious system set up within the body of Christ that sets the qualifications of a priest/minister/pastor based on their education. That is a step backward from the "order of Melchizedek" and, in fact, is a step back to the Law and away from the grace of God.