Heb. 8:6 But as it is, Christ has obtained a ministry that is as much more excellent than the old as the covenant he mediates is better, since it is enacted on better promises.
Have you ever wondered what makes the new covenant better? First it has a better sacrifice; rather than animal blood the new covenant is secured by the blood of the Son of God. It is also based on better promises. What is the better promise? The new covenant deals with the heart. Our heart is where all of our problems stem from, the new covenant not only cleanses our heart, it changes our heart. In the new covenant God’s Word is inscribed on our heart. Our very desires are changed, we actually begin to desire to know God, to love God, and to follow after His plan for our life. Andrew Murray taught about the blessing of the new covenant, here is some of what Murray said.
“The better covenant spoken of here was promised in Jeremiah: “This is the covenant I will make … I will put my law in their minds and write it on their hearts: (Jeremiah 31:33) and “I will make an everlasting covenant with them … to fear me, so that they will never turn away from me” (Jeremiah 32:40). The Lord also declared, “I will cleanse you from all your impurities. I will put my Spirit in you and move you to follow my decrees and be careful to keep my laws” (Ezekiel 36:25, 27). The promises contained in these Scripture passages are more than clear: God Himself will do the work. He will plant the desire in the hearts of His children to never depart from Him, and He will cause them to follow His laws. This is the New Covenant of which Jesus is the Mediator. Through the Holy Spirit, He lives in us to keep us from sin, so that we shall have the desire and the power to do God’s will in all things.”
This makes following Christ very simple. It is not ‘trying’ really hard to live right and to follow Christ, it is yielding our heart to the Lord. It is in yielding that the blessing of the New Covenant kicks in. What is the blessing of the New Covenant? It is the anointing of Christ within us. He writes His word in our hearts and begins to live this new life in and through us.