Apsu is the Akkadian form of Sumerian abzu, and the word names a feature of the landscape before it names anything mythological. Southern Mesopotamia sits on ground where fresh water rises: marshes, springs and a high water table beneath a plain that gets almost no rain. The abzu is that water understood as a single body underlying the earth, from which wells and rivers are fed, and it lies below rather than above.
Its owner is Enki, called Ea in Akkadian, the god of wisdom, craft and incantation, and his temple at Eridu was the E-abzu, the house of the deep. Eridu was remembered as the first city, the place where kingship first came down, which puts the freshwater deep at the beginning of the Sumerian account of civilisation as well as of the world.
The idea was built as well as told. Mesopotamian temples kept a basin of water called an apsu in the courtyard, used for purification and understood as a working image of the deep beneath. Gudea of Lagash records making one; a large stone basin from Ashur carries figures of water deities pouring streams from vessels. A priest washing before an offering was therefore not merely rinsing his hands but touching the underlying water at the point where it had been brought up. One word covers a cosmological region, a slain primordial being, a temple and a piece of furniture, and Mesopotamian usage sees no difficulty in that at all.