And having been perfected, He became the author of eternal salvation to all who obey Him, called by God as High Priest according to the order of Melchizedek." 
(Heb. 5:9-10)

Jesus is our High Priest and as our High Priest he took the sacrificial blood to the altar in heaven for us. He placed the spotless blood of the Lamb on the lid of the Ark of the Covenant that is called the Mercy Seat. (Heb. 9:12.) The blood was pure and undefiled and was the result of divine seed placed in a virgin girl.

As our High Priest, he is the only man qualified to enter the Holiest of All and he is not of the Levitical priesthood.

From the time of Moses until the time of the revelation of the Messiah, the Levitical priests took the blood of bulls and goats to the altar. Year by year on Yom Kippur, the Day of Atonement, the high priest, who was of the priestly tribe of Israel, cleansed himself and following the ritual procedure, entered into the Holy of Holies in the Temple. (Heb. 9:7.) There he spoke the name of God and through the sprinkling of the blood made atonement for the sins of the people. (Ex. 30:10.) But this earthly priesthood could never cleanse and take away forever the sin of the one who entered the Holy of Holies. The blood of bulls and goats was inadequate and so was the priest.

As Christians, the Word tells us that we are to rule and reign as kings and priests (Rev. 5:10), but if the Levitical priesthood could not eliminate sin, but rather only atone (cover) sin for a while, then it is evident that we need a better priesthood and that is what we have in Jesus. (Heb. 7:11; Heb. 9:11-14.)

Jesus was not a priest in the Levitical priesthood. In fact, He was not even from the tribe of Levi. He was from the tribe of Judah and there has never been a priest from that tribe. (Heb. 7:13-14) Jesus was not of a Jewish priesthood, but rather, He was a priest according to the order of Melchizedek. Melchizedek is not a name, but it is a title (according to ancient Jewish writings, including the Hebrew Talmud). He was the king of Salem (later Jerusalem). According to ancient Jewish writings, Melchizedek was Shem, the son of Noah, and in the genealogy of Abraham (great x 7 grandfather of Abraham). Keep in mind Abraham was 58 years old when Noah died.

Melchizedek and Abraham made covenant after the victory over the kings with bread and wine and Abraham gave a tithe to Melchizedek. (Gen. 14:18-20; Heb. 7:1-2.) While the Levitical priests received tithes under the law, Melchizedek received tithes apart from the law. In fact, the law did not even exist until 430 years later. (Gal. 3:17.)

On the day Jesus resurrected and went into heaven, He took His blood and put it on the Mercy Seat. It was the first blood ever placed there. The heavenly Holy of Holies (referred to as the original and not the copy) had not been defiled by the blood of an animal or the entrance of a sinful priest, but was pure and holy and ready to receive the perfect sacrificial blood of Jesus. When the blood touched the altar, instantly Jesus became the head of the Church. He became the firstborn among many brethren (Rom. 8:29) and our firstfruits offering (1 Cor. 15:20).

Although the Holy of Holies that contained the ark of the Covenant was built by man according to a template that was shown to Moses while he was on Mt. Sinai (Ex. 25:9; Ex. 26-27), it could not equal the original in heaven. So the perfect High Priest, Jesus, took the perfect blood (not from an earthly father) and placed it on the perfect altar in the original Holy of Holies in the heavenlies. (Heb. 9:23-26.)

So when we receive Jesus as our Lord and Savior, we submit to His priesthood which is not a priesthood under the law but under a new and better covenant based on faith and grace.

While the Levitical priesthood was for the children of Israel, our High Priest according to the order of Melchizedek is for all mankind who will receive Him as their lord and savior. While the Levitical priesthood was a shadow of things to come, our High Priest is the fulfillment of that prophecy and is the once-and-for-all permanent exclusive High Priest for all eternity.

While the Jews who believed in Jesus were redeemed from the curse of the law, the gentiles who received Jesus stepped into the new covenant having never been under the law. But for those who believe, whether we were jew or gentile, we are now one in Christ, our High Priest, according to the order of Melchizedek.