The biggest problem with the old covenant (Mosaic law) is it could never forgive sin. The constant sacrifices that were made year after year only covered sin, but never forgave them. But, Jesus did something greater. He made a single sacrifice that forgives and stands for all time. Because of that there is no longer a need for sacrifices. With this truth in hand, it should push us to godliness in our lives, instead of living a life of deliberate and continued sin.
When Jesus saves us, he calls us to a new life. We should not continue living in the same manner we did before we were saved. That is the purpose behind the warning in the latter portion of chapter 10. God forgave our sins for the purpose of sanctification, which is being made to look more like his son. So, we need to encourage one another, as Christians, to live such a life unto God.
Are you encouraging other believers in their faith walk?