Frame Story: The Lesson Within

A frame story is a story that provides a set-up for the main tale. In most instances, the tale is told within the frame story. It allows for a narrator that is either omnipotent or also a part of the tale. In most cases, the character receiving the tale learns something relevant to their current situation.

Frankenstein
The frame story in this novel is about an audacious sailor named Robert Walton. He decides that he will be the one to discover the much sought-after Northwest Passage. He journeys into the treacherous waters of the Arctic Ocean. On this trip, his crew discovers a stranger trapped on the ice. This stranger is not worried about his own safety; he only cares about catching some strange creature. He only agrees to come aboard Walton's vessel - which is his only hope of survival - when Walton says that his crew will keep an eye out for the creature. The stranger discovers that Robert Walton is as obsessively focused on a goal as he once was. He then decides to "burden" Walton with his tale.
The Lesson:
Do not let the pursuit of your goals consume your life - especially if that goal is scientific discovery.

Rime of the Ancient Mariner
A wedding-guest is on his way to a wedding in this poem's frame story, when a strange man stops him. This man is a mariner who feels compelled to share his story with the wedding-guest. The wedding-guest wishes to leave, but something in the mariner's eyes bids him to stay and hear the tale.
The Lesson:
"He prayeth best, who lovest best, all things both great and small" - in other words, cherish all life for the betterment of your own.

The Caucasian Chalk Circle
A dispute takes place between two villages in this frame story. This story takes place during World War II, when the Nazis have been pushed back, and the villagers have returned to their war-torn homes. There is a valley in between the two villages that both wish to make use of. The valley inevitably goes to the village (or, "kolcho") that wishes to advance technologically. This winning kolcho invites a singer to share a tale about a previous time of war with the visitors from the other kolcho and the government expert who is there to make the arrangements for the valley.
The Lesson:
In times of war, it is better to rally together than to tear yourselves apart.