Nefesh is the first and lowest of the levels of soul in the Kabbalistic scheme, and it is the term with the deepest biblical roots: in the Hebrew Bible nefesh means the living being as such, the throat, the breath, the appetite, and it is used of animals as well as of people, so that Genesis 2:7 has the human become a nefesh hayyah, a living creature. Kabbalah takes it as the vital soul, bound to the body and to the blood, present from birth, the seat of appetite and of the instinctual life; the Zohar treats it as the level that all possess without effort, the others being acquired or awakened. It is the level associated with Assiah, the world of action, and the sefirah Malkuth in the standard correspondences.
Later Hasidic teaching sharpened the idea further. In the Tanya of Shneur Zalman of Liadi, the founding text of Chabad Hasidism written in the late eighteenth century, every Jew is held to possess two nefashot, an animal soul, nefesh habahamit, rooted in the physical vitality of the body and capable of both permitted and selfish desire, and a divine soul, nefesh haelokit, a spark of holiness clothed within it; the moral life is described there as the ongoing contest between the two for control of a person's thought, speech and action, the three "garments" through which any soul-level is held to express itself in the world. That framing gives the oldest and most basic of the five levels a psychological complexity the earlier Zoharic material states only briefly.
Sources The ZoharTraditionally attributed to Moses de Leon with Tanya (Likkutei Amarim)Shneur Zalman of Liady