Philosopher Eward Feser explains what a soul is, but not successfully, I'm afraid.
His analysis begins with de rigueur Aristotelian-Thomistic tap dancing on the nature of things. He then locates human beings between animals and angels, evidently seeing no need to consider whether angels exist outside of human fantasy. After this, we get to human beings. Feser defines human beings by their powers to reason:
A human being is by nature a rational animal. That is to say, a human being is something which by its nature exercises both the animal powers of nutrition, growth, reproduction, sensation, appetite, and locomotion, and the intellectual and volitional powers possessed by angels.Unfortunately, Feser does not address whether studies of animal intelligence have any bearing on the last statement. For instance, ring-tailed lemurs apparently have some math abilities, and dogs are pretty smart, too. For another instance, bottlenose dolphins may experience a sense of self. For a third instance, we may have reason to think animals and humans share a similar "free will." If these instances carry any merit, perhaps we should say human beings are more rational animals or more broadly rational animals. In any case, we should be careful not to assume an absolute distinction between humans and animals in terms of intellect and volition--and we still have no evidence of angels.
Yet, without a very clear demarcation between animals and humans, it becomes difficult to isolate the essentially human soul--as opposed to the animal or vegetative souls. That difficulty, in turn, should push us to question the usefulness of the idea of a human essence, and so too a human soul. For me, a serious red flag has already been raised in the simple fact that Feser takes too much time to get to the concept of the soul. He might explain that the concept is poorly understood popularly and even by religious experts and Aristotelian-Thomistic philosophers, but this would only suggest that the concept is itself problematic.
Let's look at how Feser tries to back into the idea of the soul from human intellect and volition. He begins to isolate the soul by figuratively lopping off the human body:
a human being can be damaged to such an extent that it completely loses the organs of its animal and vegetative powers, and thus cannot exercise them at all -- to such an extent that only its intellectual and volitional powers remain. But those intellectual and volitional aspects of human nature, precisely because they are immaterial and thus do not depend on any corruptible material organ, cannot themselves perish, any more than they can in the case of an angel -- though they would be impaired given that the human intellect’s normal source of data is the sense organs, which are material, and given that its activity is normally carried out in conjunction with imagination, which is also material.Feser asserts the immateriality of the "intellectual and volitional aspects of human nature," but I cannot see the basis for the assertion--outside of assuming dualism. Yet human intellect and volition have clear ties to the functioning of the human brain, primarily. Were the brain to become non-functional, that person’s intellectual and volitional powers would cease. They would become ultimately immaterial, so immaterial as not to exist!
Feser seems to be saying that the soul, human intellectual and volitional power, is what the brain does; it is the sign of what people essentially are. Feser also insists the soul is like a material aspect of a person. For him, a person has eyes, arms, legs, hair, lungs, and a soul. It's dualism, again, but I don't get it. This is like saying a ball has both a spherical shape and motion. It's like taking an effect--intellectual and volitional power, motion--and asserting that it causes or determines the thing--a person or a ball, respectively. I thought we had grown up from the kind of thinking where we just made shit up without having to reference reality.
So, if Feser's answer is the best there is--which I am not claiming--on what a soul is, then I remain unconvinced that it is anything mysterious or outside of what we normally understand as nature.