The better covenant spoken of in Hebrews 8 is guaranteed by a better sacrifice. It is on the basis of the new and once for all sacrifice of the Son that the promise of Hebrews 8:12 can be fulfilled; and it is also on this basis that the cleansing to which the Old Testament sacrifices pointed are truly effective.

While the writer has much background information to bring to his discussion, the main focus in Hebrews 9 falls on the Day of Atonement. Nahum Sarna has pointed out that the events of the Day of Atonement provide ‘a perfect and remarkable coalescence of the most sacred individual, the most sacred space, the most sacred day of the year and the most sacred rite' of Old Testament worship (cited in M. F. Rooker, Leviticus, p. 212).

The Day of Atonement was the only occasion on which the High Priest could enter the most holy place. He was specially attired (in plain linen garments, befitting the humble and penitential nature of his action on this day) and there he could make atonement for his sin, the sin of his family, and that of the people of Israel. In addition, the ceremonies of this day cleansed the Tabernacle itself, enabling it to be the fitting venue for the continued presence of the Holy One of Israel. There were three orders of sacrifice: a bull, a ram and two male goats. Of the latter, one was chosen by lot to be the scapegoat which bore away the sins of Israel into the wilderness; the other was sacrificed within the Tabernacle. All this was accompanied by the burning of special incense and the careful manipulation of the blood of the slain beasts on the mercy seat.

Detailed descriptions of these actions can be found in Leviticus 16, which is important background reading for Hebrews 9-10. The problem is stark: to approach God without the proper sacrifices ended in death (Lev. 16:1 cf. 16:13). This is so because of the intensity of the holiness of God on the one hand, and the depth of human sin on the other. The sacrifices are needed because sin demands judgement and God cannot ignore the offence that sin is to his own nature and being. The vocabulary for sin covers all possible offences: iniquity, transgression, uncleanness, and sin (16: 16, 21). There is also an intensification of the action of substitution-with the High Priest placing both hands in confession over the scapegoat (Lev. 16:21)-whereas normally only one was used. This may indicate that it is a double sided action, in that it atoned for his sins and that of the people, but whatever the precise meaning it is abundantly clear that there was thereby symbolized a transferring of Israel's sin in its totality to this animal. The vocabulary used for ‘atonement' (kpr) means to cover, to remove from sight, and this by means of a substitute, or a death which removed guilt vicariously. The fact that the live goat was taken out to the wilderness placed emphasis on the removal of sins, taking them outside the camp, never to return. Some suggest that the place to which the goat was taken was the haunt of demonic powers, to which the goat was abandoned up in judgement.

The writer to the Hebrews makes it plain that all of this action could only ever be temporarily and symbolically effective. In the continual nature of the offerings (which seemed still to be in operation at the time Hebrews was written) the Spirit was signifying the limitations of the offerings that were given (Heb. 9:8-9). The main reason for their limitation was that they could not cleanse the conscience (Heb. 9:9, 14 cf. 9:26; 10:1-7; 10:14-18). The conscience can only be cleansed when sin is taken away, and this only happened finally in the cross of the Son of God.

The matter of conscience is deeply important, and we know well that terror that a troubled conscience brings. Calvin once said that ‘the torture of a bad conscience is the hell of a living soul'. Conscience is universal, and it is clear that all human societies and religions seek some way of atoning for guilt, removing shame and thereby cleansing the conscience. When a conscience is awakened by grace to see the true nature of sin, righteousness and judgement (which is the work of the Holy Spirit), the abject terror that this brings admits no possibility of release save through the work of the Son on our behalf. The following links take you to some fine treatments on the matter of conscience, and are highly recommended.
http://www.newcreation.org.au/books/pdf/178_ConscienceConquered.pdf
http://www.newcreation.org.au/books/pdf/099_LFS49.pdf

All other sacrifices pointed to the fact that sin needed to be judged, that there needed to be an atoning sacrifice, and that God graciously provided the substitute for us. But none of the sacrifices could finally do this. The time of the temporary sacrifices had now passed, and the consummation of the ages has brought Christ to light as the perfect sacrifice (Heb. 1:1-4 cf. 9:26). The Tabernacle/Temple not only stood for a certain period of time, it stood for (in the representative sense) a certain age which has now passed away. All religious sacrifices for all time have been rendered obsolete because of the finished work of the Son. For this reason he does not have cause to make reference to sin for his people when he returns on the last day (Heb. 9:28), since it has been put away by his sacrifice on their behalf (Heb. 9:26).