(I wrote this in a Catholic Answers forum--I'm using my blog to keep track of things I wrote)
In Genesis 3, when Adam (and Eve) disobeyed God, they were deprived of the Tree of Life (Genesis 3:22). Without the access to the fruit from the Tree of Life, man dies. God placed a fiery sword and a cherubim to guard the Tree (v.24). T
Christ restores the Tree of Life. Through Christ, we have eternal life. His Cross becomes the new Tree of Life and His Body is the fruit. We eat of His Body and we gain eternal life. Through obedience (and Baptism), we are united to Christ and through Christ and His Body, we gain eternal life.
Sin is disobedience to God. If we disobey God, we die. Christ pays for the penalty of our disobedience through His death. So, through His new covenant, we are baptized into Him and with obedience, we remain in Him (per John 15). Our sins are nailed to the cross and we are born anew so that we can rise with Him in the Resurrection.