What exactly is a persons soul?

The soul is the spiritual or immaterial part of a human being regarded as immortal. Since it is nonphysical (like preferences) it cannot be detected physically. Some are more soulful or spiritual than others.

Your soul is you - the person.

 In the Bible, "soul" is translated fron the Hebrew nephesh and the Greek psykhe.  Bible usage shows the soul to be a person or an animal or the ife that a person  or an animal enjoys.

  To many persons, however, "soul" means the immatrtial or spirit part of a human being that survives the death of the physical body.  But these is not a Bible teaching.

It's a synonym for spirit, I want to say.

Here the answer: https://www.jw.org/finder?wtlocale=E&docid=1001077299&srcid=share

It is our spiritual nature, what separates us from mere animals, which have only a biological nature, and cease to exist when they die.

There is no such thing as a "persons"  soul.  A soul does not belong to many, but to one.

Before they knew that minds were generated my brains they incorrectly explained minds as coming from souls.
Souls, of course, do not actually exist.

How about the energy of life itself. Energy cannot be created or detroyed, so what happens to that energy after death? Could that be the soul / spirit ?

There may be a fair debate on the exact meaning, but I believe that it is not your dead body, but rather yourself or your emotional self that is left over after the body is gone.
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So you can trim your fingernails and cut your hair, and have teeth pulled, and your appendix and such ...and still be 'you'.  Continue this line of thought , you can be on a ventilator and maybe an artificial heart and still be 'you'.  All your body can eventually fall apart, (or be replaced) and you would still be 'you.'.  It is you without any physical attributes (or limitations)