Cubism arose and gained popularity during the early 1900's. It's a sort of offshoot of modernism and naturalism, which also began appearing during this time. The Cubist movement was most apparent in art and literature.
It was led by painters Georges Braque and Pablo Picasso. A general characteristic of the period and genre is a rebellion against the objective and logical emphases of the previous period. Instead, Cubism places an emphasis on the subjective mental experience. That means that artists and authors would illustrate things in a way that describe how each author experienced it. Instead of narrating cold facts or drawing perfect reflections of events, Cubism allowed artists to show their own internal interpretations of things.
A result of Cubism's emphasis on the subjective mental experience is that the art and literature of the genre tend to be disjointed. For example, William Faulkner's novel As I Lay Dying tells the story from 15 different perspectives. Each with a unique voice and tone. Stream of consciousness writing also gained popularity through the Cubist movement.
Sigmund Freud's work emerged during this time period as well. His work in psychoanalysis likely contributed to Cubism's disjointed feel. Freud would focus on a person's internal struggles of the mind and even divided the human psyche into three distinct parts: the id, the ego, and the superego. Cubist authors reflected Freud's focus on internal struggles by writing stories that weren't so much about where characters went, but were more about the internal emotional struggles of characters.