Buck understands early on how the power and cruelty involved in the natural setting. The law of the club reflects this. The law of the club is how human beings subjugate the dogs. The world into which Buck is taken is a savage one, predicated upon power and submission. Organisms survive through the exertion of power and control over another. The law of the club is how human beings demonstrate their power over the dogs. Buck recognizes that there is only power, nothing close to fairness and reciprocity. The life that Buck led with the Judge is long gone and in its place is a setting where human beings enforce their will over the dogs through the club and beating the dogs into obedient submission.
The law of the fang is how the dogs internalize this element of power within one another. When Curly is killed by the other dogs, it is the fang that sustains life amongst the dogs. Life in the Klondike is regulated in how the dogs interact with one another. The law of the fang reflects this. It is a setting in which power, not fairness, governs how the dogs behave with one another. Curly's death reflects a lack of "moral consideration." The law of the fang reveals this in that the dogs do not experience solidarity or a sense of honor amongst them. The fang and seeking to avoid it is how consciousness is for the dogs in the Klondike.
Both laws underscore the world in which Buck lives. He recognizes both laws as governing his being in the world: "So that was the way. No fair play. Once down, that was the end of you. Well, he would see to it that he never went down." Buck understands that both laws dictate his survival. Living in the shadow of both the law of the club and the law of the fang is a way in which Buck learns to adapt to the world into which he has been placed.