A significant part of what the Hebrew writer has to say revolves around the truth that Jesus is mediator of a new, better covenant (8:6, 9:15, 12:24). What is involved in this?
We know from other texts (1 Timothy 2:5 for one), that Jesus is our mediator and we understand that we come to God through Him. Christ being the mediator the covenant provides us with details as to how He mediates between God and man—He does it through the new covenant.
In 7:12 Jesus is spoken of at the “guarantor of a better covenant.” The guarantor was the person who co-signed for a loan or provided bail for a prisoner. They took financial responsibility for another person. In a similar manner, Jesus takes responsibility for the new covenant. He is more than just the person through Whom God gives the covenant—He is personally involved in all for the details since it is by His death that the covenant is ratified and by His life it is assured!
It is a better covenant because of the finality of forgiveness (“I will forgive their wickedness and will remember their sins no more” – 8:13). It’s not that people weren’t forgiven under the old covenant—they were, but there was in the Day of Atonement an annual reminder of sin (10:3). The sensitive, discerning Hebrew would recognize (to some degree) the built-in limitations of the covenant; that the sacrifices that were offered were insufficient in and of themselves to afford them the status they enjoyed with God (v. 4). Contrast this with the Lord’s Supper, where we celebrate the truth that by His death (and resurrection), Christ has dealt with sin. Thus, while the sacrifices were adequate for external regulation and outward purity (9:10,13), they did little to touch the inner man (v. 9,14), and they did nothing to touch the eternal (v. 15, 11:39-40).
These truths mean that through Christ and his covenant we have a better hope by which we draw near to God (7:18). This hope anchors our soul and brings us into His presence (6:19). It is something we hold “unswervingly” to (10:23) Again, it’s not that they didn’t have hope under the old covenant, but since our hope is grounded in Christ and His work of redemption (6:19-20), it’s also equally obvious that they didn’t have it in the manner that we do.
There is both continuity and contrast in the two covenants. For example, in either covenant it is by grace through faith that man enjoys a right relationship with God. This has always been true—even before the first covenant (Genesis 15:6). While the covenants have this general principle in common, as the Hebrew writer has shown us, there is much difference in their details. Since those details have to do with Jesus and what He accomplished through His death and resurrection, they make all of the difference in the world!