As Brian grows hungrier and hungrier after the plane crash, he's willing to eat whatever he can find in the wilderness to keep him from starving. This tells us more about his situation, maybe, than it does about his character—probably anyone in similar circumstances would be just as ready to swallow raw turtle eggs or chow down on strange, sour-tasting berries. (Right?)
But what we learn about Brian's diet in his life before the crash does give us some information about who he is and how he lives. All the foods that Brian thinks of longingly while he's living on the lake—burgers, pizza, milkshakes, fries—help to characterize him as a typical kind of kid, someone that the average reader can probably identify with.
And of course, the Thanksgiving turkey and his mother's pot roast—all of the happy food memories that Brian relives in his mind—work to characterize his family before the divorce as an ordinary, normal American family.
Probably the most important indicator of Brian's character is his behavior throughout his ordeal. Maybe it's just because he doesn't have anyone to talk to (luckily he doesn't call his hatchet Wilson and start chatting it up), but for Brian, actions speak louder than words.
Although at first he's terrified and bewildered to find himself alone in the wilderness (not to mention flying a plane on his own), he does a pretty good job of staying calm and figuring things out. Over and over we see Brian looking at a problem—whether it's how to build a "food shelf," how to start a fire, or how to make a fish spear—and taking a step-by-step approach to solving it.
It's easy to imagine someone in a similar situation totally losing his cool. (Shmoop, for one, would pretty definitely be a quivering mass of nerves.) Brian, though, keeps his head for the most part, and uses anything and everything that he can find to get himself through. What we learn from this is that he's smart, resourceful, and methodical—definitely someone you'd want by your side in a crisis.
Although we don't really know exactly what Brian looks like—the narrator never directly gives us a description of him—we do get a sense of how much his physical appearance, and his physical makeup, change over the course of his time in the woods. He starts out as a pretty average thirteen-year-old kid—well-fed and not particularly used to hard work. After a few months on the lake, though, Brian's body has toughened up considerably, and he's become lean and rangy, with tanned skin and calloused hands.
As Brian himself notes, the changes in his physical appearance are a good indicator of the changes in his character. They're also a clue to how hard he's had to work to survive, and to just how different he is from the frightened kid we first met in the book's first chapter.