THE NEW COVENANT

A covenant is a binding agreement between two parties, an irrevocable decision that cannot be canceled. 

The covenant that we read about in the pages of the Old Testament is based on keeping the moral law established by God in order to maintain a right relationship with Him. The substitutional sacrifice of innocent animals was necessary to atone for the sins of the people.  

For the law having a shadow of good things to come, and not the very image of the things, can never with those sacrifices which they offered year by year continually make the comers thereunto perfect. Hebrews 10:1

This was the forerunner and 'type' of a better covenant, established when the death, burial, and resurrection of Jesus took place. He became the 'Lamb of God'.

The 'old' ushered in the 'new'.

Therefore He is the mediator of a new covenant, so that those who are called may receive the promised eternal inheritance since a death has occurred that redeems them from the transgressions committed under the first covenant. Hebrews 9:15

When we receive the gift of salvation, our immense sin debt is paid in full. We become spiritual heirs of the Lord Jesus Christ. He bequeathed to us His 'last will and testament' upon His death; all of the goodness and grace that belonged to Him is applied to our account.

Spurgeon - It was absolutely needful that guilt should be atoned for, and, therefore, Jesus became a mediator. Nothing short of this could secure the eternal inheritance for those who are called. Take away the atonement and you have robbed our Lord of His greatest reason for being a mediator at all. We love and live upon the truth of His atoning death. Whether it be a covenant or a testament, death is necessary to make it valid. God’s covenants have ever been sanctioned and ratified with blood, and the covenant or the testament of eternal grace is ratified with the blood of the Surety and Testator. 

Christ is seen both as the Will-Maker who dies, and the Executor who administers the estate ... just as He was both the offering for sin and the High Priest who offered it. 

Blessed be the God and Father of our Lord Jesus Christ, who according to His abundant mercy has begotten us again to a living hope through the resurrection of Jesus Christ from the dead, to an inheritance incorruptible and undefiled and that does not fade away, reserved in heaven for you, 1 Peter 1:3-4

An intimate Father-child relationship and the total (and continual) forgiveness of sins ... this is the inheritance that is yours if you come to the throne of grace and receive Christ by faith. 

Those who reject the offer are still under the old covenant and remain in their sin.