When Mafatu sees the wild boar in the jungle on the island, he recalls when his grandfather killed a boar and made a necklace from the teeth of the animal. The necklace symbolizes his grandfather's courage and the respect that was shown him afterwards. The killing of the boar was considered to be an act of courage and skill, two attributes Mafatu's people greatly admire. Mafatu has always remembered his act of bravery, and he tries to model himself after his grandfather.
When Mafatu faces the boar and says he's going to kill it, Mafatu tries to show the same kind of courage his grandfather did. He remembers the respect his grandfather was shown, and this encourages Mafatu even more to show no fear. He especially wants to prove to his father, the Great Chief, that he isn't the "boy who is afraid". He even makes his own necklace with the teeth of the boar he kills, just like his grandfather did.
The act of killing the boar is a turning point for Mafatu and foreshadows that his journey to manhood will be successful.