"5 Consequently, when Christ came into the world, he said,
“Sacrifices and offerings you have not desired,
but a body have you prepared for me;
6 in burnt offerings and sin offerings
you have taken no pleasure.
7 Then I said, ‘Behold, I have come to do your will, O God,
as it is written of me in the scroll of the book.’”
8 When he said above, “You have neither desired nor taken pleasure in sacrifices and offerings and burnt offerings and sin offerings” (these are offered according to the law), 9 then he added, “Behold, I have come to do your will.” He does away with the first in order to establish the second. 10 And by that will we have been sanctified through the offering of the body of Jesus Christ once for all."
Hebrews 10:5-10
The point these verses is making is not that the New Covenant abolishes sacrifices in favour of something else but that it rejects animal sacrifice in favour of that personal sacrifice God willed for Christ and for which He prepared by appointing for Him the body of His Incarnation. It is in this body that Christ fulfilled all the perfect will of God - 'Lo, I come to do Thy will, O God' (9) - and, as we have already seen this is the atoning element in His sacrifice on the Cross. The quotations here are from Psalm 40, and we may say that their particular significance is that the Psalmist saw that what God wanted supremely was obedience to His will, and perceived, however dimly, the lineaments of One Who would give that perfect obedience to God. It is by this will - i.e. by the perfect performance of it by Christ - that we are sanctified. Once more we see the parallel to the teaching of Romans, where in 5:19 Paul says, 'By the obedience of One shall many be made righteous'. It was the value of this perfect obedience in the offering of the body of Christ that made His death atoning and efficacious. Only some of our great hymns stress this aspect of our Lord's death, but those that do capture some of the wonderful depth and richness of the apostolic teaching. See Hymn 703, particularly the lines, My Saviour's obedience and blood Hide all my transgressions from view.