A soul resides in all life forms that are intelligent. It is spiritual life that is not part of any physical phenomenon.
In the world of EXTRA it is said to be the source that enables a container to have life.
In the past, in the medical community, it was thought that the body = life, and the body was an output device needed to power the soul. Without a living body, a soul could not be generated.
However, in the magus community the opposite was thought to be true. The soul is a “will” that lies in another dimension, and that will occupies a body.
Which school of thought is correct still remains unknown today, however in the world of EXTRA Pseudo-Spiritron Theory has been established. From this theory it became clear that the soul can activate even without a physical body, and as such the soul has come to be treated as “the source of a person.”

Fate/EXTRA Material: Encyclopedia of Fate/EXTRA