“For since the law has but a shadow of the good things to come instead of the true form of these realities, it can never, by the same sacrifices that are continually offered every year, make perfect those who draw near. Otherwise, would they not have ceased to be offered, since the worshipers, having once been cleansed, would no longer have any consciousness of sins? But in these sacrifices there is a reminder of sins every year. For it is impossible for the blood of bulls and goats to take away sins.” (Hebrews 10:1–4 ESV)

“And by that will we have been sanctified through the offering of the body of Jesus Christ once for all.
And every priest stands daily at his service, offering repeatedly the same sacrifices, which can never take away sins. But when Christ had offered for all time a single sacrifice for sins, he sat down at the right hand of God, waiting from that time until his enemies should be made a footstool for his feet. For by a single offering he has perfected for all time those who are being sanctified. 

And the Holy Spirit also bears witness to us; for after saying, ‘This is the covenant that I will make with them after those days, declares the Lord: I will put my laws on their hearts, and write them on their minds,’
then he adds, ‘I will remember their sins and their lawless deeds no more.’  Where there is forgiveness of these, there is no longer any offering for sin.” (Hebrews 10:10–18 ESV)

The Law (or our adherence to a moral ethic) is powerless to make perfect those who follow it.  It reveals and restrains sin, but is powerless to restore or renew.  The Law and its sacrifices are but a shadow of that which was to come, namely the perfect fulfillment of it – JESUS.  If the law could have offered true, lasting forgiveness then worshipers would not have had to continue to offer sacrifices annually, but it cannot cleanse the conscience from sin.  The sacrifices served the worshiper by reminding them of their sin, its grip on their lives and their debt to God, but the blood of bulls and goats can’t take away sin.  The entire Hebrew sacrificial system was built upon sacrifices being offered for the remission of sin, but the author is saying that the blood of animals is powerless to take away our sins – last years sacrifice won’t cover this year’s sins.  Additionally, the blood of goats and bulls can’t cleanse the conscience – a permanent solution to sin is required.  The entire sacrificial system is looking forward to the only acceptable sacrifice that would ever be offered.  Something far greater and more powerful was required to not just pay for sin, but to kill it – once for all.  Jesus’ single sacrifice was sufficient – so much so that He reigns in heaven with authority over all things.  His single sacrifice for sin “has perfected for all time those who are being sanctified.” (Hebrews 10:14 ESV)  Old Testament believers were saved the same way that we are – by placing their absolute trust in the provision of God for their salvation.  God does not delight in sacrifices and offerings, He is after hearts that are fully His.  The sacrifices had no intrinsic value in and of themselves – the value was in communicating the costliness of sin and the extreme price that would have to be paid to deal with our treasonous hearts.  We are sanctified (made holy and grow in holiness) by the sacrifice of Jesus Christ.

As a result of the singular sacrifice of sin, God has now fulfilled the promise to write His laws on our hearts and minds.  This means that we now desire to know God, follow Him, and obey Him – though not perfectly, but with a new affection for Him that the law was powerless to produce.  Anytime we become dependent upon the law to prove ourselves righteous, try to change, or earn God’s approval, we fail because law based living is powerless to take away sins.  Only the grace of God and the new heart that desires to know and obey God produces lasting transformation.  Which of these most accurately reflects your faith:  1) I obey because it is my responsibility, God says to, it will make God happy with me, to earn His approval, to pacify His wrath, to increase His love for me, to work Him into my debt so that He owes me or the more faithfully I obey, the more God will bless my life.  2) I obey because God loves me unconditionally, did not spare His own son to redeem me, set His redeeming affections upon me before He placed a star in the sky, I am perfectly loved and accepted by God because of the sacrifice of Jesus or I want to know Him more and see His glory.  We’re forgiven, the alter is closed, your sacrifices are not accepted.  “Where there is forgiveness of these, there is no longer any offering for sin.” (Hebrews 10:15–18 ESV)  We look to Christ for our growth and perfection.  He has earned it for us.  Instead of personal, hard fought, self disciplined effort, the believer looks to Christ for a cleansed conscience, complete forgiveness, power to change and complete perfection in the future.  For we will be made perfect – our rebel hearts will be overthrown (Hebrew 11:40, 12:23)