It’s worth noting that the letter to the Hebrews were written to Jews who because of persecution by their own people, were being tempted to turn their backs on Jesus and return to Judaism.
And so the whole theme throughout this letter is that in Jesus we have something better, superior to anything Judaism had to offer.
You actually see that word several times. In Jesus, we have a better hope (7:19), a better covenant (7:22; 8:6) that is based on better promises (8:6). As a result Jesus has a superior ministry to that of the Levitical priests (8:6). Not only that, he himself is a better priest because he is sinless and lives forever, in contrast to priests that were sinful and ultimately died (7:23-28). He ministers in a greater and more perfect tabernacle (9:11). And the sacrifice he offered was better than any bull or goat (9:23), because his sacrifice actually could cleanse our hearts and consciences before God. The sacrifices of bulls and goats couldn’t do that. That’s why the priests’ work in offering sacrifices never stopped. But after Jesus offered himself on the cross, he sat down at the right hand of God. (9:9-10, 13-14, 10:4-12, 14)
In the tabernacle, only priests could enter the Holy Place, and only the high priest could enter the Most Holy Place. (9:1-8)
But now, we who belong to Jesus have access into the holy places and our Father who dwells there. (10:19)
Best of all, our relationship does not depend on how faithful we are to him. It depends on his faithfulness to us. (Hebrews 8:10-13, 10:23).
That’s why we can have confidence before him. Not because of who we are. But because of who he is.
I can put it no better than the writer to the Hebrews.
Therefore brothers and sisters, since we have boldness to enter the sanctuary through the blood of Jesus–he has inaugurated for us a new and living way through the curtain (that is, through is flesh)–, and since we have a great high priest over the house of God, let us draw near with a true heart, in full assurance of faith, with our hearts sprinkled clean from an evil conscience and our bodes washed in pure water. Let us hold on to the confession of our hope without wavering, since he who promised is faithful. (10:19-23)