Vardaman Bundren in William Faulkner's novel As I Lay Dying is a six-year-old child, brought up in an eccentric family living in the rural south, who has just been traumatized by the death of his mother. His stream-of-consciousness reflects the though processes of a child, rather than the rational thought patterns of an adult.
Vardaman remembers an occasion when he caught a fish and cut it up into pieces. At that point, it stopped acting like a fish. The pieces no longer demonstrated fish-like behavior such as wriggling or swimming. Thus the fish, after being dismembered, was both a fish and not a fish.
Vardaman does not really understand death as an abstract concept, but rather only dimly understands that his mother, like the fish, is no longer really his mother. He does not quite comprehend why; thus he drills a hole in her coffin to help her breath.
The phrase which Vardaman repeats, "my mother is a fish," is his version of saying that his mother is dead, just as the fish was dead, despite his not having a vocabulary or intellectual framework including the abstract notion of death.