"The Elephant's Child" is one of Rudyard Kipling's Just So Stories for Little Children, published in 1902. Like the other tales in that collection, it's an "origin" or pourquoi story—a playful fable that invents a fanciful explanation for how something in nature came to be, in this case why elephants have long trunks.
The name comes from the way Kipling first told these tales aloud to his own children, especially his eldest daughter, Josephine. When telling a bedtime story that a child knows and loves, the child often insists it be repeated in exactly the same words every time—no changes, no shortcuts, no improvised variations. Kipling's children reportedly demanded that each tale be told "just so," precisely as before, with every familiar phrase and rhythm intact. That insistence on exact repetition gave the collection its title and helps explain the stories' distinctive style: the chanting refrains, repeated phrases, and rolling cadences (like "the great grey-green, greasy Limpopo River") are all features of stories polished through being retold again and again in the same form.