If most books show you a totally finished building with a nice façade, Woolf is giving us a tour of the construction site.
Mostly, authors work hard to make you forget that the fictional character is just words on the page. But here's Woolf, introducing her fictional narrator: "call me Mary Beton, Mary Seton, Mary Carmichael, or by any name you please—it is not a matter of any importance" (1.2), because "Mary" is "only a convenient term for somebody who has no real being" (1.1).
And when we get to Fernham, Woolf pauses again to remind us that she's making this story up: "I dare not forfeit your respect and imperil the fair name of fiction by changing the season" (1.23). Just as we're ready to kick back and enjoy the story, she reminds us that she's in charge. She's not changing the season because it would be jarring to us, but she could if she wanted to.
Where normally an author would simply introduce the character, Woolf is more interested in showing us the inner workings of fiction than trying to get you to suspend disbelief. Basically, she's pulling back the curtain.
So, when we say this style is "self-conscious," by the way, we don't mean that Woolf is shy, or anything. We mean that the style of writing is self-conscious: as you read, the text keeps reminding you that you're reading a piece of fiction created by another person. So, what does this have to do with Women and Fiction?
Woolf's insistence on the five hundred pounds a year and the private room are about the very practical things that make fiction-writing possible. So maybe this self-conscious style is a kind of practical illustration of the writer's task. We're not just reading a story, we're seeing how a writer works.