The word hamartia occurs very frequently in the book of Hebrews (25 times), and 10 of these uses are found in chapter 10 alone. Not surprisingly, most of the references have to do with the sacrificial system, which was set up because of sin.
The Son of God, when He came to earth, did so in order to purge our sins (1:3). He was made a merciful and faithful high priest, in order to make reconciliation for the sins of the people (2:17). We have a high priest who knows what it is like to be tempted, even though He was tempted without sin (4:15). This is something that a high priest does, it is part of their calling — sacrificing for sin (5:1), not only for the people but also for his own sin (5:3; 7:27). But Christ, as high priest, has really dealt with sin by His sacrifice of Himself (9:26). Christ was offered once to bear the sins of many (9:28), and at His second coming He will appear without sin for final salvation (9:28).
We are told to exhort one another, as long as it is called today, that we not be hardened by the deceitfulness of sin (3:13). We are promised that one of the terms of the New Covenant is that God will no longer remember our sins (8:12). The promise is repeated again in the tenth chapter (10:17).
In the Old Covenant, the repeated sacrifices meant that the worshippers were not really being cleansed from sin in any final way (10:2). In every sacrifice there is a remembrance that sin is still around (10:3). It is not possible for the blood of bulls and goats to take away sin (10:4). God had no pleasure in the sacrifices for sin found in the Old Testament (10:6). God did not want such sacrifices for sin (10:8). The priests of that time offered up repeated sacrfices, which could never take away sin (10:11). But Christ dealt with sin once for all, and then sat down at God’s right hand (10:12).
Whenever real remission occurs, there is not more need for offerings for sin (10:18). If we return to the Old Covenant forms after being told of Christ — the once for all sacrifice — we are returning to a system that has no efficacy, no sacrifice for sin remains (10:26).
Moses choose to be with God’s people rather than to enjoy the pleasures of sin for a time (11:25). And since we are surrounded by the great witnesses spoken of in chapter 11, we must lay aside every sin that besets us (12:1). We have not yet resisted against sin to the point of shedding our blood (12:4), and this is something we should be prepared for.
The bodies of animals slain in the sacrificial system, whose blood as for sin (13:11), were burned outside the camp. And Christ Himself was slain — outside the camp so that we might be allowed into the city.