In chapter 7 of Hatchet, Brian, still feeling ill from the "gut cherries," happens upon a bush of much more palatable raspberries. While picking them, he hears a noise. He soon sees that the source of the noise is a full-grown black bear standing only a few yards away. The bear, who had also come to eat the raspberries, stands up on its hind legs to study Brian. It then ignores Brian and goes back to its business of eating the berries.
Upon seeing the bear, Brian instinctively takes off running. After a bit, Brian stops and realizes that the bear is not chasing him. In fact, it is not interested in him at all. Eventually, Brian talks himself into going back for more berries.
This event teaches Brian that he need not fear the wilderness if he is careful and can keep his wits about him. While there certainly are dangers, not everything, not even huge bears, are necessarily out to harm him. All the same, Brian keeps his hatchet handy that night in case the bear comes looking in his shelter for more berries.