"Robert Walton" is what can be called "a plot device." In other words, his character is not central to the story of Dr. Victor Frankenstein and the creature Frankenstein created, but rather serves as a logical means by which the story of Dr. Frankenstein can be conveyed.
Mary Shelly understood that, if the story of Dr. Frankenstein's pursuit of his creation is to be memorialized and conveyed to future generations, a third person had to be involved to bear witness and hear first-hand the story of the monster's creation and subsequent conflict with its creator. As the story of that pursuit ends in the desolate Arctic region, there would be nobody to find the doctor and hear his story of the monster's creation, and of his moral conflict over whether he had a right to bring such a creation to life, unless another human could somehow be on the scene. Consequently, the character of Robert Walton serves that purpose. By placing an explorer, who stays in contact with his family through a series of correspondence, at the scene, the story of creator and creation can be relayed to the outside world.