Neshamah is the higher soul, the third of the five levels, from the Hebrew for breath or the divine soul, and the breath God breathes into the first human at Genesis 2:7, nishmat hayyim. Kabbalah takes it as the intellective and intuitive soul, the seat of higher understanding and of the direct awareness of God, holding that it is awakened by study and by the fulfilment of the commandments rather than possessed by nature; the sources speak of it as a level many never attain. It is associated with Beriah, the world of creation, and with Binah. The three-level scheme is the one the Zohar works with most, and Gershom Scholem traced its development and its relation to the Neoplatonic material that reached Jewish thought through Arabic philosophy.
A distinct and much older idea attached to this word is the neshamah yeteirah, the "additional soul" the Talmud (Beitzah 16a) says every Jew receives for the duration of the Sabbath and loses again at its close. The custom of smelling fragrant spices at havdalah, the ceremony marking the Sabbath's end, is traditionally explained as a consolation for that loss, reviving a soul suddenly diminished. The idea is talmudic rather than Kabbalistic in origin and predates the Zohar's graded five-level scheme by roughly a thousand years, but later Kabbalistic writers folded it into the neshamah level specifically, reading the weekly gift of an additional soul as a small, recurring taste of the higher awareness the level as a whole represents.
Sources The ZoharTraditionally attributed to Moses de Leon with Major Trends in Jewish MysticismGershom Scholem, Encyclopaedia Judaica, 2nd editionMichael Berenbaum and Fred Skolnik (eds.)