Jesus Christ work of purging sin is superior to times past
The word ‘purge’ katharismos means ‘to cleanse by purging out the undesirable elements’ and when Hebrews refers to the purging of sin, it refers back to the Old Testament sacrificial system, especially, the Day of Atonement in Leviticus 16 (ex: Hebrews 9:24-26)

Definitions for the Day of Atonement (Leviticus 16):
The sin offerings were offerings of propitiation, or appeasement for sin
The burnt offerings were offerings of atonement, or covering for sin
The scapegoat was an offering of expiation, or removal of sin

Christ’s work was superior because He was perfect (Leviticus 16:1-6)
If Jesus Christ ever sinned once in thought, word, deed, intention, motivation, etc; He would have not been able to offer an acceptable sacrifice to God (Leviticus 22:17-25)
Christ’s work was superior because it was sufficient (Leviticus 16:7-10, 20-22)
Propitiation and atonement are incomplete without expiation (ex: sweeping dirt under a rug doesn’t get rid of the dirt)
But even all 3 of those sacrifices was insufficient (Hebrews 10:1-4, 11-14)

* In order for this superior work to be applied to us, we must constantly afflict our souls (Leviticus 16:29-31)
This word means to humble oneself
To humble ourselves in mourning and repentance (Psalm 35:11-14, James 4:8-10)
To humble ourselves to understand God’s words (Daniel 10:10-12)