Hebrews 9:13–14, Purifying the flesh…cleansing your conscience. The Levitical sacrificial system was never able to atone for sin in the full sense. These sacrifices were effective only temporarily in that they had to be continually repeated.
In reality, these sacrifices never mitigated YHVH’s judgment against sin. The Levitical sacrifices simply covered over sin, so that the sinner could stand before Elohim without being consumed by his righteous judgments. But only Yeshua’s death could satisfy Elohim’s judgment against sin permanently in the life of the believer. Only his atoning sacrifice can thoroughly wash away our sins, remove the death penalty, which is the wages or penalty of sin, and cleanse the sinner of the guilty conscience which resides in his personal spirit, so that one could “serve the living Elohim” with a clean slate.
Sin can contaminate the spirit of man, which houses the conscience of man (2 Cor 7:1; see notes at Col 3:10). Only the blood of Yeshua can miraculously cleanse our soul (the mind, will and emotions) and spirit of a person and bring us to perfect holiness in the fear of Elohim (ibid.) This Yeshua did in a spiritual sense in the spiritual temple in heaven, which is greater than the physical temple on earth, which was a mere copy or shadow of the one in heaven (Heb 8:3–6).
The cleansing that the Levitical sacrificial system offered was physical and external, while the one Yeshua offers through the heavenly temple gives internal cleansing.