Brian's mother gives him a hachet before he takes the plane to go see his father in Canada. It's important because the hatchet is the whole point in the book, the only thing that will allow later Brian to survive in the wilde.
I know it's difficult for you that your father and I are getting a divorce but can't you tell me what's really bothering you ?
The plane in whom Brian was travelling crashes in the Canadian wilderness because of the sudden death of the pilot. Brian's completely alone and has only the hatchet. This is the real start of the book, the reason why Brian will have to learn how to deal with the wild to survive.
Brian finds berries for food. When picking some he meets a bear but it made no move to attack Brian. By this enconter, the boy learns that wilde animals "made no move to hurt you, to threaten you" and that's the beginning of multiple lessons that Brian will learn during his journey in the wilde.
When Brian discovers after the encounter with a porcupine, that the hatchet was the key to make a fire, he perseveres and successes making one. This is important because it's another of the lessons that Brian learns : don't give up, keep trying and trying in order to success and survive.
A tornado destroys eveything that Brian has built, including most part of his shelter and his environment. He keeps hope and shows courage even if only the hatchet remains. This event proves that the wild made Brian stronger and definitely more brave. He should be an exemple for all of us.
After the tornado the plane reappears at the surface of the lake. Brian suddenly remembers that there's still the survival pack in it. He decides to go get it and after many difficulties sucesses. He finds inside an emergency transmitter and is rescued. These events are important because they are the end of the book, when the climax falls ans when the conclusion is made.