The part of their being that died instantly was their spirit. The death of their spirit separated Adam and Eve, and therefore mankind, from God. Without a living spirit within to communicate with the living God, a relationship was not possible.
In a cascade effect from sin entering in, the fall of mankind impacted all of creation. God cursed the creation and the redemption of the universe is tied to the redemption of mankind.Whoa!
God Is The Only Source Of LifeThe Spirit of God is the source of life. Sin destroyed the spirit of man and the effect was a soul and body that although not dead began a process of expending the life that was present, unto a final death.
And you were dead in your trespasses and sins, in which you formerly walked according to the course of this world, according to the prince of the power of the air, of the spirit that is now working in the sons of disobedience. - Ephesians 2:1-2 NASB