In The Jungle Book, the "Law of the Jungle" is a set of rules by which the civilized animals conduct their lives and business. Since the animals are more intelligent than in real life, they are able to codify and create a set of rules to govern their behavior; the rules are based in pragmatism and instinct, since some of the animals are not as civilized, and wild nature dictates a level of response to attack, rather than reasoned argument or discourse. A good example is the prohibition against killing Men:
The Law... forbids every beast to eat Man except when he is killing... man-killing means, sooner or later, the arrival of white men on elephants, with guns...
As shown, this Law is bad in pragmatism, since indiscriminate killing of Men means large-scale retribution. In the end, animals will fall to Man's guns, so it is better to not incite Man with random killings.
Another example is punishment; to the animals, there is no sense in grudges if the Law is broken. When Bagheera's honor is damaged by Mowgli's actions, the law dictates that Mowgli be punished, despite his regret; however, this punishment acts to wipe the record clean, and there is no resentment.
One of the beauties of Jungle Law is that punishment settles all scored. There is no nagging afterward.
(Kipling, The Jungle Book, Google Books)
Other Laws are explained in the text through action and by Baloo, who serves as teacher; each Law acts on the story, dictating how Mowgli grows and learns to live with the animals according to their rules and instincts. Mowgli's own instincts are of Man, and so he thinks differently, but he understands the need to abide by the Law, despite his own instincts to the contrary.