The Many Names and Meanings
Over time, Apsu gained many names. In one of his original incarnations, the dragon was feminine, which was why he had the name Zigarun, which was Akkadian for "The Mother who has Begotten Heaven and Earth." 
Apsu was another Akkadian name, and he was also known as Apason and Rishtu.  In Assyro-Babylonian mythology, he was known as Apzu,  in Sumerian mythology, Abzu.  To the Babylonians, he was Aphson. 
According to the ancient wisdom of Mesopotamia, all life came from the water.  At first, Apsu was perceived as a feminine entity, but he later became a personal god, the husband-dragon of Tiamat and the father of the first deities.  Apsu was the personification of the sweet water ocean that ran under the earth,  for he was the ruler of all fresh water. 
In the great creation myth recounted in the Enuma Elish, in the beginning, there was no earth or sky, only the waste and confusion  of the primordial oceans existed.  Apsu was the sweet water that encircled the earth, and he fused with the female principle, Tiamat,  the personification of salt water.  This was the beginning of creation: 
When sweet and bitter mingled together,
No reed was plaited, no rushes muddied the water,
The gods were nameless, natureless, futureless,
...from Apsu and Tiamat,
in the waters gods were created,
in the waters silt precipitated.
-- Enuma Elish 
In some accounts, Apsu and Tiamat could not bear the noise and uproar caused by the younger gods, and so Apsu planned to eliminate them.  But other versions claimed that the rebelliousness of the new deities angered Apsu and his wife  or that Apsu overheard his children plotting to kill him. 
Whatever the cause for his alarm, Apsu decided to stop his children,  and he and his wife called upon Mummu for assistance. Tiamat, despite her anger, declined to kill her descendants when Mummu and Apsu joined forces. 
Thus, the struggle between the old, primordial deities and the new order began.  In the Babylonian creation epic, Enki killed Apsu with either magic weapons  or a magic incantation, then locked Mummu away.  In other versions, Enki cast a spell on Apsu, setting him into a deep sleep, so that the deity could kill the monstrous dragon-god. 
Pulled down the bar and posted guards.
He squared Apsu's quarter, the abode of Nudimmud,
As the lord measured the dimensions of Apsu.
The Great Abode, its likeness, he fixed as Esharra,
The Great Abode, Esharra, which he made as the firmament.
Anu, Enlil, and Ea he made occupy their places.
-- Enuma Elish 
Apsu as a Sacred Place
The word 'apsu' sometimes referred to a sacred place in the watery depths, where Apsu the dragon dwelled and later the god Enki resided.
As a place name, apsu was used to refer to the extensive sweet waters that produced the southern Mesopotamian marshlands when it became the home to the wise god Enki  and the birthplace of Marduk. 
Apsu was the counterpart of Tiamat, but he was rarely described. Since he completed the destructive dragon, he was also seen as a dreadful serpent.
- Apsu was the personification of the sweet water  and ruler of all fresh water. 
- He was the husband-dragon of Tiamat and the father of the first deities. 
- He became determined to stop his children from rebelling,  but his wife refused to kill them. 
- Mummu aided Apsu in his quest to quiet the younger deities. 
- His struggle with his offspring became the war between the old, primordial deities and the new pantheon. 
- Enki cast a spell on Apsu, setting him into a deep sleep, and then slew the monstrous dragon-god. 
- His death caused Tiamat to revolt  with an army of monsters and renegade gods to avenge her spouse's death.