Why does Mary Shelley include Walton's letters to Mrs. Saville in Frankenstein?

With Walton's letters Mary Shelley creates a frame story and uses it to have one narrative play off another. The introduction of Walton and his inner thoughts and passionate desires to conquer an extreme challenge in his letters generates a perspective that is similar to that of Victor Frankenstein and mitigates to some extent the outlandishness of Victor's desires, helping to suspend the disbelief of readers. There are parallels between the two men: both are extreme in their goals and desirous of doing what no other man has done; they are self-driven and obsessed with their goals.

These letters and the frame story, in the end, find their sequel in the tale of Victor Frankenstein’s experiences leading up to and after the creation of the monster. This frame story affords Shelley an easy transition into the last days of the long-isolated Victor Frankenstein, a man who is driven to destroy his monster but also feels the need for confession.  

Mrs. Saville is a passive receptor of information and actions, like the other female characters who all play secondary or passive roles. Justine, for example, the only noble character in the novel, passively accepts the false accusations against her and her subsequent death. These passive and minor roles are not unlike that of Mary Shelley herself, who often sat listening to discussions between Lord Bryon and her husband. In fact, some feminist criticism interprets Shelley's lack of any dynamic female characters as a criticism of her time and even her marriage:

The absence from her novels of independent, self-fulfilled, nurturant women records Mary Shelley’s oblique recognition that such a woman does not survive in the world she knew. (Mellor, 1989: 210)

While Frankenstein should not be interpreted as semi-autobiographical, it does contain some parallels to Mary Shelley's life and the people surrounding her. Such parallels suggest that there was an underlying purpose to Frankenstein's narrative. 

What might be Mary Shelley's purpose in starting Frankenstein with Walton's letters?

Mary Shelley uses a frame story to set up her novel Frankenstein. This allows readers to move into the story from the perspective of an observer, and it helps establish a particular viewpoint and some of the story's themes. Let's look at this in more detail to help you get started.

Letters are personal documents that offer a personal perspective that approaches Frankenstein's tale from the outside before getting into the depths of it. Robert Walton writes to his sister of his voyage and his hopes of discovery in the realm of the sciences. He is greatly excited by his journey yet longs for some close friend who can share it with him. He speaks of Coleridge's poem "The Rime of the Ancient Mariner" to express the fears that blend with his excitement. As the voyage begins, Walton looks toward and longs for success.

Notice the themes that these letters are introducing. We encounter the longing for scientific exploration, a desire for intimacy and friendship, and a nod toward the supernatural. We find ambition and excitement and confidence.

Then in the fourth letter, we receive a tantalizing hint that begins to zoom into the main story. Walton catches a glimpse some huge man on a sledge. Then he finds a half-frozen man, whom he takes aboard his ship. It is Victor Frankenstein himself, and we get the impression that we are about to hear quite a tale. The author has raised our curiosity. The story is set. The themes are introduced. Now Frankenstein's story can begin.