Story told to illustrate a moral or spiritual truth

One word substitute is Parable.

Didactic: intended to teach, particularly in having moral instruction as an ulterior motive.
Parable: a simple story used to illustrate a moral or spiritual lesson, as told by Jesus in the Gospels.
Paragon: a person or thing regarded as a perfect example of a particular quality.
Paradigm: a typical example or pattern of something; a pattern or model.