The writer of Hebrews gives us the essence of the New Covenant in today’s Bible reading: “I will put my laws into their minds, and write them on their hearts, and I will be their God, and they shall be my people. And they shall not teach, each one his neighbor and each one his brother, saying, ‘Know the Lord,’ for they shall all know me, from the least of them to the greatest. For I will be merciful toward their iniquities, and I will remember their sins no more.” (Hebrews 8:10-12, quoting from Jeremiah 31:31-34)
The problem with the Old Covenant is that God’s people repeatedly broke the covenant. God knew they would and planned the New Covenant from the beginning. Because of the depth of our lostness, the depth of our depravity, God knew that He would have to keep both ends of the covenant. So under the New Covenant, God puts His Holy Spirit in every believer to empower us to live up to His standards and to even give us the desire to live up to His standards. God did it all!
God knew the hearts of His people. And He knew the ones we inherited from our first parents couldn’t keep the Old Covenant. So He told the Old Testament prophets that He would cut a New Covenant with His people. Not only would He cut a New Covenant, but He would also give circumcised hearts to His people, hearts that would be able to — and desire to — please Him. (Ezekiel 36:26–29)
And I will give you a new heart, and a new spirit I will put within you. And I will remove the heart of stone from your flesh and give you a heart of flesh. And I will put my Spirit within you, and cause you to walk in my statutes and be careful to obey my rules. You shall dwell in the land that I gave to your fathers, and you shall be my people, and I will be your God. And I will deliver you from all your uncleannesses. And I will summon the grain and make it abundant and lay no famine upon you. (Ezekiel 36:26–29 ESV)