Summary: The superiority of Jesus' priesthood gives us boldness to approach the throne of grace.
GREAT HIGH PRIEST
The priesthood of Jesus is superior to that of Aaron. As a man like ourselves, Jesus is a merciful and faithful high priest: yet, unlike Aaron, He is capable of facing and overcoming temptation on our behalf (Hebrews 2:17-18; Hebrews 4:15). For though He is a man, Jesus is also the Son of God (Hebrews 5:5).
The earthly tabernacle is only a shadow of the heavenly (Hebrews 9:11-14). The sons of Aaron needed to repeat their sacrifices and offerings over and over again, according to a complex ritual: morning and evening, Sabbaths, new moons, festivals; day by day, month by month, year by year. Jesus has provided the one full final perfect sacrifice for sins, once and for all and for ever, by His own blood (Hebrews 9:24-26).
Jesus’ priesthood is of a better order than that of Aaron (Hebrews 5:10; Hebrews 7:11). It is not genealogy which qualifies our Great High Priest, but the power of an indissoluble life (Hebrews 7:16). Jesus has passed into the heavens (Hebrews 4:14) - and is set on the right hand of God (Hebrews 8:1) - and there makes continual intercession for His people (Hebrews 7:25-27).
This gives us boldness to approach the throne of grace (Hebrews 4:16).