Romans 5:12-13 meaning

After Adam sinned (Genesis 3) death spread to all men. Therefore, just as through one man sin entered into the world, and death through sin, and so death spread to all men, because all sinned (v 12). We have all sinned (Romans 3:23). As a result of that sin, death spread to all men. That means that every single human is affected. Thus, all of humanity experienced death through sin.

Death in the Bible often means separation. We use the term death in English in the same way. When we say a relationship has died, it means the people who were connected are now separated. Spiritual death resulted from Adam's fall. Along with Adam and Eve, we as humans are all spiritually separated from God, with no means within our power to heal the separation.

Sin is living apart from God's (good) design. Sin leads to death, which is separation from God's (good) design for creation. This affects every person, because all sinned.

We are born being separated from God; we are "dead in our trespasses and sins" (Ephesians 2:1). We are made alive through the resurrection power of Jesus, received by faith (Ephesians 2:1).

The first physical death Adam and Eve experienced for themselves included exile from the Garden (Genesis 3:23). Exile is a separation. Adam and Eve also experienced the death of an animal to create a covering for themselves (Genesis 3:21). They experienced a break in their legal relationship with God when they broke the one rule He gave them to follow (Genesis 3:17). They also experienced a break in their fellowship with God as they hid from God (where they previously would have met Him to walk and talk together, Genesis 3:10). Adam and Eve experienced a breach in their relationship, as evidenced when Adam blamed both God and Eve rather than accepting responsibility (Genesis 3:12).

Later, they experienced the physical death of one son at the hand of another son (Genesis 3:8).

Even though we who have believed are now standing in the grace of God as being righteous before God, we still live in a world that is yet to be fully redeemed, a world that is full of sin and death. Just as sin and death entered the world through one man, life and freedom from the wrath of sin also came through one man, the God-man, the second Adam, Jesus (Romans 8:12, 15).

Jesus came to provide deliverance from the penalty, as well as the power, of sin. When we believe, we are freed from the penalty of sin immediately. We are then given the Spirit to indwell in us, as well as the resurrection power of Jesus to be able to overcome the power of sin in our daily lives when we walk daily by faith. Eventually, Jesus will return to earth and permanently vanquish sin and death, thereby fully redeeming the world (Revelation 21:4).

Paul adds for until the Law sin was in the world, but sin is not imputed when there is no law (v 13). After Adam and Eve fell, the Law was not yet given—that came much later, through Moses. Even so, as the next verse states, death was in the world from then until when Moses gave the Law.

An application here seems to be that the consequences of sin are in effect even when people live in ignorance. However, the text says that sin is not imputed when there is no law. The word translated imputed is also used in Philemon, where it is translated as "charge" as in the phrase "charge that to my account" (Philemon 1:18). It is the idea of creating an obligation. The point here is that people cannot be charged with breaking a law that does not exist.

In spite of that, death was in the world notwithstanding. Death is the consequence of sin. Any sort of sin produces some sort of death, some variety of separation. Perhaps it is separation of relationship. Perhaps a separation of someone from their potential. In a severe case, someone's spirit separates from their body; this is physical death. Paul is building up to the fact that we can be immensely grateful that God did not leave the world in this sad state. Rather, He came to redeem it through the advent of a great and marvelous gift—the free gift of eternal life through faith in Jesus.