Mrs Dalloway is the ultimate example of modern literature (meaning it is part of the genre of modernism). After World War I, people felt like their world was shattered, and art and culture went through dramatic change. Writers and artists of all kinds began to question the traditions of the nineteenth century. Thinkers embraced new ideas like cubism (think Picasso’s messed up faces) and surrealism (think of a melting watch). It was a very creative time, and an era in which new media such as photography and cinema arrived and changed the way people saw the world.
Take a moment to compare Mrs Dalloway to, say, any Charles Dickens novel – perhaps Great Expectations. Rather than having a straightforward narrative with a beginning and end and a narrator who knows it all, with Mrs Dalloway we have several narrators, flashbacks, stream-of-consciousness style, and a totally fragmented story. As a modernist, Virginia Woolf rejects the idea of a linear storyline that many writers had used in the past, and she rejects the idea that one being who "knows all" tells the whole story. Part of her point is to demonstrate through the book how life has changed after the war: life is not so neat and tidy anymore.
To oversimplify (and maybe make things more complicated all at once): remember how Clarissa feels about Sir William Bradshaw? That he's oppressive and authoritarian, and only wants things done in the English and traditional way? That’s sort of how Virginia Woolf felt about traditional storytelling.