The New Covenant is better than the Old Covenant (Heb 7:22; 8:6). It is better because it was established on better promises (8:6, 8-12); it has a superior High Priest (7:11, 20-28); it has a greater and more perfect tabernacle (9:11); under it a better sacrifice was offered (9:23; 10:1-4, 11-14). It is to this better sacrifice that the writer of Hebrews now turns his attention (9:16-28). Remember, the reason the author demonstrates the superiority of the New Covenant is to dissuade those persecuted Jewish Christians of the first century from returning to life and faith under the Old Covenant. It is a covenant under which they could never be completely and eternally forgiven of their sins.
The sacrifice of Jesus Christ is far superior to those sacrifices offered under the Old Covenant (9:23). The blood of bulls and goats no matter how often it was shed could never take away sins (10:1-4). By contrast, Christ did not offer Himself often, but suffered “once” to put away sin by the sacrifice of Himself (9:26). So Christ was offered once to bear the sins of many. To those who eagerly wait for Him He will appear a second time, apart from sin, for salvation (Hebrews 9:28).