For there is one God, and one Mediator between God and men, the Man Christ Jesus, who gave Himself as a ransom for all, to be testified in due time (1 Timothy 2:5-6)
Priests are kind of a universal phenomenon. In any religion, the priest or priestess is the person with the special ability to connect with the gods (or God) in order to serve them and instruct others in how to worship and serve as well; they are mediators and ministers between the divine and humanity. Even in an atheistic society, scientists could be considered priests since they’re the ones who specialize in discovering and teaching the “ultimate truth” of empirical science.
In the Old Testament, when God gives the Law from Mt. Sinai and forms Israel as His special nation, He chooses the tribe of Levi to be the priestly tribe. They would minister in His Presence (the Tabernacle/Temple), led by Moses’ brother Aaron and his descendants, the high priests. To be a priest was a great honor and privilege because it granted you the ability to enter into the Holy Place in order to serve God, where others would die if they entered because of the awesomeness of His manifest glory. The high priest did everything the priests did, as well as entering into the Most Holy Place on the Day of Atonement in order to sprinkle blood on the Mercy Seat (representing God’s throne) in order to cover over all Israel’s sin! Old Testament priesthood was centered around access to the Lord’s inaccessible Presence and intercession on behalf of the people of Israel through sacrifices.
All of this was a foreshadowing (or “type”) of Jesus Christ and His ministry. When the Son of God comes on the scene and dies on the cross, something unspeakable happens: the Veil separating the Holy Place from the Most Holy Place is torn clean in two. This has massive implications, the biggest being that the death of the Messiah has opened up universal, free access to God’s presence! In other words, Jesus is the Ultimate Priest because His sacrificial death fully atones for the sins of anyone who places their faith in Him, allowing them to come directly to God in prayer through Him. He is the reality to which the OT priesthood points to, especially the high priest.
So how does this apply to us as disciples? If we all have direct access to the Father through Christ, and are called to serve as His representatives to the world, that makes us all priests! In Christ, we are all priests, with Him as our Great High Priest who intercedes for us before God (Hebrews 7:25). The sacrifices we offer are our own lives in obedience and worship, because Jesus gave Himself as the ultimate, perfect sacrifice once and for all on the cross.