The soul — in the esoteric tradition represented primarily by Theosophy and the Alice Bailey/DK corpus — is the sixth layer of the human constitution: the causal body, so called because it is the body that carries the causes that determine the conditions of each new incarnation. It is the layer of the self that is genuinely individual (unlike the Oversoul, which is a group reality) and genuinely enduring (unlike the personality, which dissolves at physical death).
The soul is not a fixed entity but an evolving one. It grows through incarnation — each lifetime adding to its accumulated experience, refining its understanding, developing specific qualities and capacities that it did not have before. The soul at the beginning of its evolutionary journey is barely differentiated from the group soul of its oversoul; the soul at the end of its evolutionary journey is a fully individualised, radiantly developed being capable of conscious co-creation with the divine. Between these extremes lies the entire journey of human spiritual development across many lifetimes.
In Vedantic terms, what corresponds to the soul is the Atman — though Vedanta tends to emphasise the Atman's identity with Brahman (the universal) rather than its individuality. In Kabbalistic terms, the soul corresponds to the Neshamah — the divine breath that is breathed into each being, carrying the spark of divine intelligence. In the Seth Material, what corresponds to the soul is the "entity" — though Seth reserves this term for what we would call the Oversoul. The terminological variation across traditions is real; the underlying reality they are pointing at is consistent. There is something that persists, something that grows, something that individualises further with each incarnation and that carries across the gap of death.