Let Me Tell You a Story

"Now, this is a story all about how My life got flipped, turned upside down And I'd like to take a minute, just sit right there I'll tell you how I became the prince of a town called Bel Air!"

Alice and Bob are having a conversation. Alice wants to make a point, but to tell Bob straightforwardly wouldn't have the impact she wants to make. So she decides to tell him a story. The story at first seems somewhat random and unrelated to the matter at hand. However, once the story is finished, it becomes clear that there is a moral behind it. If Bob still seems confused about the story's relevance, Alice may spell it out for him. Or she may just leave him guessing.

The most common term for these stories is the parable, a tale used to illustrate some message. The term often refers to religious parables meant to express spiritual concepts. Of course, it's not limited to that.

Old people are very prone to do this, often in the form of a Rambling Old Man Monologue. They have a lot of stories to tell.

The musical version of this is Morality Ballad. See also And That Little Girl Was Me.

"Margaret: When I was a girl in Ireland, a raggedy man would come around every spring with a little Bantam rooster. He'd trained it to peck out "The Mountains of Mourne" on a toy piano hung off his chest. Lucy: So? Margaret: Well... the first year he came, we all of us, the girls in that place, we thought it magical. The second year, we laughed behind our hands at the odd man and his tatters, and the third year we didn't even go, because "The Mountains of Mourne" was all that little rooster could ever do. Lucy: So what's the point? Margaret: That maybe your cunny... isn't quite the draw you think it is."
 * The parables of Jesus are among the most famous examples. Jesus would often tell stories to convey his messages.
 * Also in The Bible (2 Samuel 12), the prophet Nathan tells a story to call King David to repentance for sleeping with Bathsheba and sending her husband Uriah to his death. In the story, a rich man with many sheep slays a poor man's only lamb to feed a guest.
 * Happens a lot in Boardwalk Empire. For instance, Margaret tells this to Lucy after Lucy brags that all she has to do is spread her legs to keep Nucky interested:

"Alfred: A long time ago, I was in Burma, my friends and I were working for the local government. They were trying to buy the loyalty of tribal leaders by bribing them with precious stones. But their caravans were being raided in a forest north of Rangoon by a bandit. So we went looking for the stones. But in six months, we never found anyone who traded with him. One day I saw a child playing with a ruby the size of a tangerine. The bandit had been throwing them away. Bruce: Then why steal them? Alfred: Because he thought it was good sport. Because some men aren't looking for anything logical, like money. They can't be bought, bullied, reasoned or negotiated with. Some men just want to watch the world burn."
 * In The Dark Knight, Bruce Wayne is trying to figure out The Joker's motivations. Alfred tells him this:

"Alonzo: I'm saying that to say this. Soon as you think you've seen everything out on these streets, these streets will teach you something twisted."
 * In Training Day, Alonzo's friend Roger decides to tell rookie officer Jake a joke. He tells him about a snail that gets thrown off some guy's porch into the backyard and nearly dies. However, it recovers and after awhile it gains enough strength to crawl again. After about a year, the snail makes it way back on to the porch. The man comes out, looks at and says, "What the ****'s your problem!?" Jake laughs until he sees Roger and Alonzo's serious expressions and realize that it isn't a joke at all. Roger tells him that when he figures the joke out, he'll figure the streets out.
 * Also, there is a deleted scene where Alonzo tells Jake of one of his early work experiences involving a black man who was paid by another man named "Spooky" to beat up a doberman he was raising. Alonzo came across the man with his fellow officer, who was completely accepting of it and explained to Alonzo that Spooky was teaching the dog to hate black people.

"Kopaka: I'm still waiting for the part where the heroic Toa Lewa saves the day!"
 * Jolee Bindo is prone to this in the Knights of the Old Republic game.
 * A favorite tool of Sophia's in The Golden Girls. Sometimes subverted when her story ends up having absolutely no connection to the matter at hand.
 * Silent Bob's Title Drop speech in Chasing Amy about his relationship with a girl named Amy probably qualifies as this.
 * The 1993 The Three Musketeers film: "Love? Let me tell you about love."
 * In the Quantum Leap episode "Jimmy", Sam leaps into a mentally retarded man in the 1960s. Eventually he freaks out in frustration, since he's being treated like an idiot all day. Casanova Wannabe Al interrupts him mid-rant: "There was this girl named Trudy..." Sam snaps at him that this is no time for another irrelevant, sleazy sex story -- but this time, the girl in question was Al's younger sister, who was also mentally retarded.
 * In the Italian mystery novel The Terra Cotta Dog:The police officer protagonist is invited to meet with Tano the Greek, a feared gangster (and Gayngster) who turns out to be something of a Noble Demon. To explain why he wants to turn himself in, Tano tells this story about a guy who bet someone that he could make a cat eat some very spicy mustard- the method involves Ass Shove-ing it, causing the cat to start licking the mustard because of the pain. The point of the story is that Tano is being threatened by a younger generation of gangsters and so turning himself in (and getting a Luxury Prison Suite) is the better option- like with the mustard,turning himself in is a bad option that becomes a good one when a worse option comes along.
 * In Bionicle, Lewa does this to Kopaka and Onua. He explains his plan by telling them the story of the three Matoran, the Rama swarm, and thebasket of Bula berries. Cue Kopaka getting more and more annoyed at Lewa because they're in the middle of a battle.

"Tab: Son, I'm gonna tell you a story about a young man who came here and failed. Well, that is the story. I shouldn't call a sentence a story. Anyway, it's you!"
 * In Daughter of the Drow, a warrior amuses a drow mage (who saved him from carnivores and tried to claim as a slave) with a folk tale about how "old favors are soon forgotten". Then.
 * SpongeBob SquarePants: Mr. Krabs' story to SpongeBob about spending a dollar on a soda to persuade SpongeBob to let his seahorse go.
 * Parodied in the Simpsons episode "The Heartbroke Kid", when Bart is sent to a fat camp and Tab Spangler, the camp owner, catches him pigging out: