This excerpt was taken from the book The Call of the Wild, by Jack London. The story is about a dog that, being stolen from a family and a comfortable life, quickly learns how to become a leader and to fend for himself as a sled dog.
The sentence in the excerpt may be paraphrased in the following manner:
London says that masters and their dogs grow attached to each other, in spite of dogs being just animals, and that masters enjoy talking about how good their dogs are.