Look, a rock is made of nothing but atoms, and so is your body, and my body. So is everything on Earth, and so are the stars in the sky. When you destroy something, you are destroying its atoms. Do you understand that?
Atomic destruction refers to the ability of destroying atoms, which has been shown by nearly every warrior in the many incarnations of Saint Seiya, starting with the original series.
Atomic destruction is very well known among saints and other groups that need to train each new generation, and consists in the destruction of atoms. As atoms form everything from a person's body, to the air, the water, the light, and everything else in the known Universe, the ability is highly versatile.