The second death is only mentioned by name in the book of Revelation. However, as a theme, it winds throughout the Bible, always lingering in the background. But to see this, we need to understand how the Bible uses the term “death.”
There is a physical application as well as a spiritual implication, and it requires discernment to understand how the word “death” is being used in a given context. The physical application is simply the end of a human being's life, whether through age, disease, accident, or violence. The breath of life leaves the person, consciousness ceases, and the body begins to decay. This is the fate of all human beings.
But the Bible also uses death to describe the spiritualstate of people who are undoubtedly physically alive. Notice Romans 5:12: “Therefore, just as through one man sin entered the world, and death through sin, and thus death spread to all men, because all sinned.”
The death that entered the world through Adam's sin was not physical death. Adam was a flesh-and-blood human being, so his body was naturally subject to entropy. The fact that he was created as flesh meant that, at some point, his heart would stop, and the breath of life would leave. Even if he had lived a sinless life, he still would have died when his body ceased to function. Adam was never immortal; he needed to eat of the Tree of Life to live forever (Genesis 3:22). When Adam sinned, he immediately entered a state of spiritual—not physical—death, which contributed to the foundation of Satan's deception that life continues after sin.
As it remains today, Satan's treachery was effective and destructive because, like Adam, we typically live on—physically—after sinning. While Adam's physical death was a foregone conclusion due to his being fleshly, it was not the death that entered the world through his sin. Instead, spiritual death entered the world at that point and spread to all of his offspring. His sin destroyed the union mankind had with God(see Isaiah 59:1-2), without which there is no life. Accordingly, separated from God, mankind has no future beyond physical death unless God acts. The wages of sin is eternal death, and there will not be everlasting life unless God gives it as a gift.
Later in the same context, Paul substitutes the word “condemnation” for “death”:
And the gift is not like that which came through the one who sinned. For the judgment which came from one offense [Adam's sin] resulted in condemnation, but the free gift which came from many offenses resulted in justification. . . . Therefore, as through one man's offense judgment came to all men, resulting in condemnation, even so through one Man's righteous act the free gift came to all men, resulting in justification of life. (Romans 5:16, 18)
Adam did not physically die in the instant he sinned, but at that moment, he was brought under eternal condemnation. This is why Jesus said things like “let the dead bury their own dead” (Matthew 8:22; Luke 9:60). Those who had not been called into a relationship with God were living in a state of death—condemnation—despite going about the normal activities of life. These people were devoid of spiritual life; they were the spiritual “walking dead.”
A major reason for Christ's incarnation was so that mankind could be redeemed from this state of death—condemnation—and given an opportunity for eternal life. Thus, He says, “If anyone keeps My word he shall never see death” (John 8:51). The Jews did not grasp His meaning: Those who keep His Word will never see eternal death; they will not lose the eternal life that comes from knowing the Father and Christ (John 17:3) following the Father's call (John 6:44, 65). However, He implies that those who have His Word and do not keep it will return to a state of condemnation.