Modernism is broadly applied to "writing marked by a strong and conscious break with tradition" (Holman and Harmon, A Handbook to Literature, sixth edition). Modernism represents a literary period in which authors are disenchanted with the time period preceding it and rebel and explore and experiment with ideas and techniques which previous "masters" would have frowned upon.
Modernism is considered experimental and different from what one had been accustomed to before WWI. There are many characteristics which apply to writing that fits in this category, although the writing may not evidence of every single one of them to be considered "modernist." Some of those include a sense of alienation, loss, despair, and focus on the individual rather than society as a whole. Modernism tends to reject traditional ideals and conventions. In many ways, it is a rebellion against realism and naturalism. Stream of consciousness in Virginia Woolf's work as well as the sexual content of D. H. Lawrence and other subject matter that was considered questionable would fall into this category. The work of T. S. Eliot ("The Wasteland") and George Bernard Shaw would qualify as Modernism, as would the psychological theories of Freud and Jung.
I have included some other sources on this type of criticism and writing for you to peruse. Good Luck!