Reproducing Chris's letters and postcards serves two major purposes in the text. First, it allows a better insight into Chris's mind; since he is not around to explain his motivations, the only knowledge of Chris anyone has is their personal memories or what they can glean from the letters. These are in Chris's own hand, straight from his own thoughts, and so they are the clearest representation of his ideals and goals that can be shown.
The second purpose is to form a better time-line of Chris's journeys. His only explicit goal was the wilderness of Alaska; otherwise, he had no fixed travel plan. Because of this, his travels are sketchy and without the letters explaining how long he stayed in a place there would be little idea of where he spent the time between locations.
From a letter McCandless sent to Jan Burres, we know he spent July and August on the Oregon coast, probably in the vicinity of Astoria, where he complained that "the fog and rain was often intolerable."
(Krakauer, Into the Wild, Amazon.com)
These snippets of Chris's writing show both his own intelligence, his deeply considered thoughts about the state of society and his own growth, and the emotional connections with others that he tried to deny, but undeniably shared.