Modernism was an experimental form with a focus on language and interiority. It reacted to and rejected the Victorian and Edwardian emphases on describing external characteristics of a place or character in an objective manner. It also often rejected the omniscient narrator. Instead, it put an emphasis on the subjective interiority of individual characters' experiences and the limited way they perceived the world.

As mentioned in the answer above, To the Lighthouse is a highly subjective stream-of-consciousness novel told primarily through the minds of its characters. I would add that it also experimented radically with time. Most of the novel—hundreds of pages—covers just one day, while in Part II, ten years pass in a few pages. Part III comprises just a morning. This reflected Woolf's sense that time was difficult, if not impossible, to capture in words. As she put it in the novel:

The urgency of the moment always missed its mark. Words fluttered sideways and struck the objects inches too low.

The above quote is important because it speaks to the modernist sense of the inadequacy of language to convey truth. Modernists like Woolf were more likely to embrace Nietzsche's idea of language as a prison house we are trapped in rather than the Enlightenment idea of language as a clear windowpane looking out onto reality.

Modernism is best described as a literary and artistic period from the first half of the twentieth century.

Modernism’s roots are in the rapidly changing technology of the late nineteenth century and in the theories of such late nineteenth-century thinkers as Freud, Marx, Darwin, and Nietzsche.

While many writers and artists from this period are now considered to be "modernist", at the time they were working there was no cohesive "modernist" agenda, aesthetically or ideologically. 

Given this caveat, we can still talk about why some writers are considered to be "modernist" and what generally characterizes Modernism.

Writers who are now considered to be representatives of Modernism often presented a significant subjectivity in their narratives. Using multiple narrators and narrative perspectives (Woolf; Faulkner; Dos Passos), creating unreliable narrators (Fitzgerald) and presenting highly opinionated narrators (Hemingway) are some of the methods used to render subjectivity in the ficiton of modernism.

In To the Lighthouse, Woolf narrates the novel through multiple perspectives, each of which fosters a different view of not only how to live, but in its understanding of what is real. This interest in subjective realities is emphasized in the content of the work with the philosophical conversations regarding the nature of objects and also in the style of the work. 

Written from multiple perspectives and shifting between times and characters with poetic grace, the novel is not concerned with plot.

Stream-of-consciousness narration is a considerable tool for achieving this end as well. This special kind of narration allows the writer to eschew objective realities to some degree and render a narrative voice that is unencumbered by fact, instead being shaped by emotional and psychological forces. 

This is certainly the case in Woolf's novel, To the Lighthouse. 

Associated primarily with Woolf and James Joyce this technique was a way of representing the whole mind of an individual, not just conscious thought.

Stylistically and ideologically, the notion of subjectivity in the narrative now characterizes the works of those writers considered to be representatives of Modernism. This narrative subjectivity can be seen as being related to a growing interest in Freudian psychology. 

Additionally, an interest in a personal relationship to history and to culture characterizes many works of Modernism. Many characters and poems from the works of Faulkner, Eliot, Pound, Joyce, Woolf, Hemingway, and Fitzgerald are either concerned with artists and writers or are fixated on personalizing elements of the past.