How we change what others think, feel, believe and do
Tell a parallel story that helps explain the main story.
Use metaphor, analogy and other forms of similarity.
The parallel may be used to fill in additional detail or add extra meaning beyond that given in the main story. This may also be a two-way affair, with each embellishing the other. Beyond this, a counterpoint structure may be used (as in music) where the stories deliberately conflict and dance around one another.
Parallels may also be made between early and late parts of the same story.
The parallel story and its meaning may be realized by the main characters, or it may be just for the story audience.
The rustics in Shakespeare's A Midsummer's Night's Dream put on a play within the play.
A story is told within the story that has uncanny relationships with original story events.
A conflict at home parallels a conflict at the office. The protagonist learns to resolve one through the other.
We do not always get the full gist of a story first time around. When it is repeated, we may well understand more.
When there is a chance that the audience will not understand the main story then a parallel may be used to reinforce key points and paint an additional picture.
Written as an entangled pair of equal stories, the device becomes an integral part of the story, adding complexity to confound and delight the audience.
The second story may also form a mirror, perhaps harking to imaginary stages in life.