Things have categories. There is the form of a hydrogen atom. The form of a dihydrogen monoxide molecule. The form of a rose. The form of a dog. The form of a human being.
Each category shares the same form. What differentiates individuals within the same form is the matter that makes it up.
All material beings are two co-principles, neither of which can naturally come into being on its own without the other: form and matter. You cannot have matter without form (aka prime matter) or form without matter. The soul isn’t itself some immaterial thing driving or cohering to the matter, it is just a principle by which a being must exist. It is also related to essence (there’s a higher level of co-principles within Thomism: essence and existence. Form and essence are pretty much the same, but we use form for material beings in which multiple individuals exist within the same category).
Now we arrive at the puzzling aspect of the human being and the “immortal soul” and what happens after death. All other beings, living or not, have their forms disappear after death/destruction. They do not persist immaterially.
What’s different about humans? Our rational minds. All other processes can be explained materially. However, the rational mind includes immaterial processes. Again, this is not some ghost controlling the material body, but immaterial processes working with and relying on material processes in tandem, bothing making up the functioning of a rational human being.
I’m going to sidestep a moment. If I cut off your hand, the rest of your body would still have the form of a human being, even missing the part or function granted by this hand. If I cut off all of your limbs, the remaining living parts that persists as the self would still have the form of a human being. If I were to cut you off from the neck down, leaving only the head kept alive by machinery, the persistent self that remains, acting as one whole being, would retain the form of the human being. What happens at death? It’s like cutting off the rest of the material parts. They no longer persist as the self, but the mind does. And the mind retains the form of a human being. It’s the immaterial mind that retains the form.
There’s actually some debate in Thomism on this last point. I disagree with the next part, but some say that this immaterial mind can no longer properly be called a human being in the way I said it when devoid of all matter, but that it will still exist and eventually be restored to the body Still, I gave my thoughts on that above.
I think a mind deprived of all its material senses would be quite handicapped. It’s not a ghost that would be suddenly freed from material and suddenly gains new powers and is unbound by material limits. That would be silly. It would lose its natural sources of sensory (name removed by moderator)ut, for one. What I would say is that, through divine intervention and sustenance, the impact of such handicaps, while they still exist, are incomparible to the glory of what God can give.
Anyway, I went a little off topic on form. I suggest picking up Edward Feser’s short book, Aquinas. I hope others can explain it better.
Oh, and whenever I talked about the form of a plant or a dog or a human, you can substitute the word soul. A soul is just the proper word used for form when the being in question is alive.