Simply put, this is any situation where a character has to force a smile or a please/thank you despite not really wanting to do so.
A few examples:
1) Character A will demand something from Character B. Character B refuses to oblige their request until Character A says "please". Character A begrudgingly does so, and only then does Character B perform the requested action. This is commonly seen between parent and child, though it can occur between adults (typically for comic effect).
2) Character A will want something from Character B. Character B refuses to give it to Character A until they give them a little smile to show their appreciation. Typically, Character A will put on a very forced smile.
It's most common in sitcoms, but can appear in dramatic works occasionally, such as if a villain is trying to smugly exert their power over the hero.
Examples:
- Everybody Loves Raymond: In "Hackidu", Ray is impatient to get out of Russell's shop with the Scramisaur card, but before Russell will let him have it, he demands, "Let's have a little smile." Ray struggles to force a smile, and after Russell says, "That's what it's all about, man", he says he owes him well over $200 for the purchase.
- In "The Christmas Picture", Ray tells Robert to get over into the picture.
Robert: What?
Ray: Get over there.
Robert: "Get over there..."
Ray: ...Please?
Robert: There ya go, Raymond. You'll find a little courtesy goes a long way.
- The Simpsons: A variant occurs in "Black Widower" when Sideshow Bob is chewing out a hotel bellboy:
Sideshow Bob: I WANTED A ROOM WITH A FIREPLACE, YOU BLASTED MONKEY! (realizes Selma is capturing him on camera) Oh Selma dear... I was just chatting with my good friend... (looks at his name tag) Dennis! Now, smile for the camera, there's a good lad! (Dennis struggles to produce a nervous smile)
- Teen Titans: Robin is being forced to take a supervillain's daughter to her prom.
Kitty: And would it kill you to smile?
Robin: Maybe.
- Subverted in The Dresden Files, where Harry is trying to negotiate a deal with local crime boss Johnny Marcone.
Marcone: Say "please".
Harry: Please...
Marcone: Say "pretty please".
Harry: Pretty please...
Marcone: Say "pretty please with a cherry on top".
- Subverted in one episode of Rugrats, where Angelica has taken a ball from Tommy, who wants it back.
Angelica: Say "please".
Tommy: Give me my ball!
Angelica: Say "pretty please".
Tommy: Give me my ball!
Angelica: Say "pretty please with sprinkles".
Tommy: Give me my ball!