"The Storyteller" begins with an aunt who is trying and failing to control her nephew and two nieces in a railway carriage. She attempts to keep them quiet by telling them a story about a good little girl, loved by all who knew her, who "was finally saved from a mad bull by a number of rescuers who admired her moral character."

The children are bored by the story and become even more fractious, whereupon a man traveling in the same carriage remarks on the aunt's lack of success as a storyteller. When she takes umbrage at this, he proceeds to tell the children a story about a good little girl who won a great many medals for good conduct. The story ends with the girl hiding from a wolf, who discovers and eats her when her medals clink together.

The man's story is a satire on the type of story the aunt told. Although this is not related at length, it is the type of moral fable that abounded in Victorian and Edwardian nurseries, in which vice is punished and virtue rewarded (Eric, or Little by Little and Sandford and Merton are prime examples of the genre). Initially, it seems as though the man's story will be as dull as the aunt's, until he uses the phrase "horribly good" to describe the heroine of the story. The sort of arbitrary details found in fairytales and moral fables are also satirized in the absurd extemporized details of the story, such as the fact that there were no sheep in the prince's park "because the Prince's mother had once had a dream that her son would either be killed by a sheep or else by a clock falling on him. For that reason the Prince never kept a sheep in his park or a clock in his palace."

How is Saki's "The Storyteller" both convincing for children and a satire?

Ironically, in "The Storyteller," it is the inner satiric story that exemplifies more about the art of storytelling than its frame story, while providing more insights about human nature as the children recognize "a ring of truth" in the bachelor's story and pronounce its ending as "beautiful."

The children enjoy the bachelor's story because it breaks from the stodgy. Having been raised by a rigid aunt himself, Saki ridicules the oppressiveness of the social ritual of preaching good behavior and social graces by having his bachelor storyteller break from traditional narratives in appealing to the sadistic innateness of the children. For, it is the very goodness--"horribly good"-- of the little girl that causes her demise as her medals for good conduct, obedience, and punctuality clink against each other as she hides from the wolf, drawing his attention back to her as his prey. 

In addition, Saki has his storyteller triumph over the mundaneness and respectable self-interest of the aunt through the power of his imagination. When, for instance, the bachelor tells the children there were no sheep in the park of the Prince, he seems to have failed with the children and the "aunt permitted herself a smile...almost...a grin."  However, he quickly recovers with a deft imagination:

"There were no sheep...because the Prince's mother had once had a dream that her son would either be killed by a sheep or else by a clock falling on him...."

The aunt suppressed a gasp of admiration.

With his imaginative story, then, the bachelor satirizes convention as he proves that what is morally instructive is not always interesting to children.