Assiah is the fourth and lowest of the Four Worlds, the World of Action or of Making, the world of matter, the physical universe, and everyday human deed. It is the point at which the emanation that began in Atziluth is fully manifested and made dense; its sefirah is Malkuth, the kingdom, and the level of soul that belongs to it is nefesh. In the Lurianic system it is also the world in which the kelippot, the shells or husks left from the primordial shattering of the vessels, are most active, and in which the work of tikkun, repair, is chiefly done. That last point is the theological weight of the scheme: the lowest world is not a place of exile to be escaped but the place where the repair of the whole is carried out, through the commandments and through intention.
Assiah takes the Tetragrammaton's final Heh as its letter and, in the Golden Dawn's London attributions, the element Earth and its own colour scale. Later Kabbalistic and Hasidic writing, developing the Lurianic material further, holds that each of the four worlds itself contains a smaller fourfold structure, so that Assiah has its own inner Atziluth, Briah, Yetzirah and Assiah; on this reading even the lowest world's own highest reach touches emanation, and the physical world named by asah is sometimes distinguished from a subtler "Assiah of the angels" active within it, the plane on which the practical, protective and healing angel-work of the tradition is chiefly said to operate.
Sources The ZoharTraditionally attributed to Moses de Leon with The Golden Dawn: The Original Account of the Teachings, Rites, and Ceremonies of the Hermetic Order of the Golden Dawn, 6th editionIsrael Regardie, Physician of the Soul, Healer of the Cosmos: Isaac Luria and His Kabbalistic FellowshipLawrence Fine