Sin means we separate ourselves from God. Because God is the living God and the source of life, sin results in death. This is similar to a piece of technology being unplugged from its power source; it continues to exist, but it is functionally dead. In the same way, the Bible says that because of sin, we are physically alive but spiritually dead. Furthermore, we will all die physically, just as God promised Adam and Eve in the garden.
Genesis 2:17; Romans 6:23