Two aspects of Virginia Woolf's background reveal her purpose in writing "A Room of One's Own." First, Woolf was denied advantages that her brothers and other men of their class were routinely rewarded. For example, while both her brothers went to college, the family did not feel it could afford to send Virginia or her sister. There were opportunities at that time for women to earn degrees from Oxford or Cambrdge, but the family assumed the women would simply get married and be supported by their husbands. Woolf was very angry at the opportunties she was denied, especially as her father acknowledged she was the brilliant one in the family.
Second, Virginia inherited money from several sources, mostly notably a Quaker aunt named Caroline Stephen, and this money, though not much, enabled her to have a room of her own in which to write. She saw the vast difference this made in her life and in her ability to become a successful writer who stayed true to herself.
In her essay, she argues that women had not produced great literature because they had fewer opportunities and next to no privacy. (She also argues that it is not because they are less capable than men--a common assumption at the time.) She points to Jane Austen, for instance, having to write her novels in a dining room while being subjected to frequent interruptions. In her own life, Woolf was an example of what a woman could do with an independent income and a room of her own. Think how much more woman could accomplish, she argues, if they could have the same university experiences as men and have more money and more privacy.