An explanation of “soul” according to my interpretation of the Bhagavad Gita:
Within every body lies a soul, an eternal essence, a piece of God. A soul is not an autonomous individual, it is the part of God that observes and experiences life from within the body.
But often times, a particular soul, being so absorbed in its observation, starts to believe itself part of the visible world. It’s so captivated, that it becomes trapped within a cycle of rebirth.
In other words, when a soul thinks itself an active player in life, consumed with selfishness and self-importance, its confusion binds it to this world. Upon death, this soul leaves the body to enter a new one, retaining an imprint of its previous lives, life after life.
But those on a path back to God, strive to remove this imprint. Once the stain is removed, the soul becomes perfect and indistinguishable from God, merging seamlessly back into God.
While embodied, to keep itself pure and unbound, the soul must realize its separateness from the visible world, understanding its relationship to God — it must passively observe, watching as the body lives out its life, not believing itself an active participant. And through many lives, the soul may attempt to perfect itself, retaining its progress from life to life, eventually leaving the cycle of rebirth.
Note: within this explanation, God is defined as the entirety of the universe, including the unseen eternal aspects, as well as the creative force that sets the universe into motion and sustains it.