What purpose does the dog serve in this story? How do London's descriptions of the dog reveal its function in the story?

The man does not belong in this setting. He can only maintain his existence by the artificial means of building fires. The dog, on the other hand, does belong in this setting because it is not far removed from its wolf ancestors who had adapted to these cruel conditions over thousands of years of struggling for existence.

At the man's heels trotted a dog, a big native husky, the proper wolf-dog, grey-coated and without any...

The man does not belong in this setting. He can only maintain his existence by the artificial means of building fires. The dog, on the other hand, does belong in this setting because it is not far removed from its wolf ancestors who had adapted to these cruel conditions over thousands of years of struggling for existence.

At the man's heels trotted a dog, a big native husky, the proper wolf-dog, grey-coated and without any visible or temperamental difference from its brother, the wild wolf. The animal was depressed by the tremendous cold. It knew that it was no time for traveling. Its instinct told it a truer tale than was told to the man by the man's judgment.

Jack London uses the dog throughout the tale to serve as a contrast to the inexperienced man. The dog does not understand its master's behavior but obeys him because of a combination of fear and trust. It is an ironic situation because the animal knows how to survive under the coldest conditions, whereas the man, who supposedly has superior intelligence, makes one blunder after another. The dog is especially useful as a character because it keeps its eyes steadfastly on its master, watching his every move, evidently trusting him to get them both to safety. This enables the author to describe the man both subjectively from the man's point of view and objectively from the dog's point of view. The dog shows loyalty right up to the end. Loyalty is part of its heritage of instincts; whereas the man has no loyalty to the dog but tries to kill it just to warm his frozen hands. The reader is left feeling more respect for the dog than for his master, who is left dead in the snow.

Jack London's use of the dog as a second character makes his story more dramatic, even though dog and man cannot communicate. The alternative would have been to use an intrusive narrator to explain the things the dog knows by instinct. There is some of that kind of intrusive narration in the story, but there would have had to be much more without the dog.