Sure, I can explain. I'm not Christian either, but I think it's pretty decipherable.
It is first important to note that it's the Grim Reaper speaking, the man who controls the taking of lives. All souls, or all existences, belong to him, because he is the one who comes and kills you when you die. He's stating that your father's soul, his father's soul, etc, as well as your son's soul, his son's soul, etc, all belong to him, the Grim Reaper.
The last part, the soul who sins shall die is important because the Bible talks about how every single person sins. That means that every soul belongs to death himself, the Grim Reaper, our namesake.