What you call a soul is composed of substances, just as your physical body is. These substances are just as complex as the molecules and cell structure your physical body is composed of - in their own way. However, these substances cannot be destroyed by such things as atomic explosions or even entry into a black hole. The soul is durable and indestructible. Souls are born, and evolve and grow, just as in your physical world you find plants and animals springing up from seed, from a single cell. This does not happen haphazardly, and only happens on worlds in 3rd Density. When an entity is incarnate, what you call the soul suffuses with the physical body, spreading throughout all the parts of the physical body.
The existence of the soul, that part of a human remaining after the physical body expires, has been measured as a tiny adjustment in the weight of the dead body, happening at the moment of death in most cases. We say in most cases, as the soul may depart earlier, seeing the trend. For instance, where individuals go Out-Of-Body during trauma, the soul has already left. Nevertheless, there is some small scientific aspect to support the general human perception that they have a soul. In fact, so prevalent is this feeling or belief in humans, that one stating the opposite comes in for some heat. Religions invariably espouse the soul and an afterlife as a reality.