God’s covenant with Adam is crucial because it reminds us of the importance of covenants in the Bible. The Bible, in many ways, can be described as a series of covenants.
Another way of thinking about covenants is as a structured relationship. God has relationships with His creation. The relationship God had with Adam was a relationship with the man made in His own image, and it was structured on the basis of obedience. God said to Adam as His created son, “Do this and you shall live,” and Adam failed.
In Adam’s failure, we see the human dilemma, but we also see the anticipation of God’s redemptive work because Christ comes as the second Adam. Christ comes to fulfill the covenant that Adam failed to fulfill. Christ comes as the Son, the second Adam, and as the one who does perfectly keep the law of God and perfectly keeps the law of God in our place.
So, the Adamic covenant is very helpful for us to understand conceptually more of what it is that Jesus has done for us and what He has done in our place to redeem us and to reconcile us with the Father.