How can the author's biography affect his work?
Some writers choose to write stories that are completely divergent from their own biography. Writers of supernatural, fantasy, science fiction and horror stories are probably writing from their imagination, not from their own experience. Which isn't to say that who they are and their point of view on life doesn't affect their writing, it simply isn't the foundation of these sorts of work.
I think that we must be very careful, when we analyze works of fiction in an attempt to make a connection to the writers biography. Art isn't as simple -- whether it be writing novels, plays, short stories, or poems (or creating paintings, dances, or music) -- as looking to the life events of the creator and deciding that we, from the outside, can determine where the inspiration comes from.
The Greeks believed that Art (including writing) was inspired by the Muses. These were goddesses who blew the inspiration into the creator and gave birth to the idea that became the work. This notion that inspiration just arrives, that it isn't the culmination of the creator's life experiences, is as valid as considering the author's biography when searching for an explanation for creative genesis of ideas.
In general, one can make the argument that an author's life impacts their work and style. If it is accepted that a writer writes what is seen and what is experienced, then this becomes the fundamental way in which the work expresses these realities. For example, if a writer experiences war, this will profoundly impact the work created. A writer might choose to use the writing as a way to make peace with this reality, or simply believe that the experiences endured make for a narrative to which others can connect. In the end, the writer composes thought on what was experienced and endured and within this is the reason why the biography of an author is so important. We write what we know, what we see, what causes us pain. If this becomes true, understanding the background or context of an author becomes vitally important.