Indeed, under the law almost everything is purified with blood, and without the shedding of blood there is no forgiveness of sins. (Hebrews 9:22 ESV)
Hebrews chapter nine examines the sacrificial system of the Old Covenant. These ancient rites dealt with external actions, not the internal conscience (cf Heb. 9:10).
Sacrifice and blood were the essential ingredients.
The priest and people repeated these ceremonies day in and day out, year after year.
The New Covenant also involves blood, but instead of the blood of animals, it is the blood of Christ. Because of his special status, his self-sacrifice on the cross is able to be a once-for-all sacrifice (cf Heb. 9:12). This does much more than purify our bodies, it purifies our minds (cf. Heb. 9:14).
So, Christ's sacrifice accomplishes everything the old sacrifices did, but more completely.
The sacrifice described in this passage is certainly a blood sacrifice, but the blood of Jesus accomplishes things animal blood never could. There is one sacrifice instead of many, and a cleansing of even our consciences instead of merely our bodies.
This is the kind of sacrifice that results in justification and paves the way for salvation.
It is clear that Christ was able to offer himself as a perfect sacrifice as a result of his submission to the Father.
Although our own discipline of submission is a kind of sacrifice, it is not the justifying kind. We are not–nor will we be in this life–perfect.
Yet, our disciplined, sacrificial submission reminds us of our own weakness and dependence on Jesus’ self-emptying actions. It furthers the process of salvation from sin in our lives, and brings us closer to each day to the ultimate goal: perfect union with God.