Perhaps someone is letting loose a torrent of profanity. Perhaps there's a streaker running past. Whatever the case, there are children around, and they are being exposed to some highly inappropriate content. Quick! Cover their eyes/ears!
Usually it's a parent who will do this. They and the children might be characters in their own right, or they might just be one-offs who are there for the sake of a gag.
Compare Not in Front of the Kid.
A Running Gag in Chobits. Every time Hideki acts strange in public, a woman's voice can be heard telling a child "Don't look at him, honey."
One episode of Tenchi in Tokyo has Ayeka, Sasami, Ryoko, and Ryo Ohki watching a soap opera. When the action onscreen starts to heat up, Ayeaka blushes in embarrassment and covers Sasami's eyes, who then covers Ryo Ohki's eyes. Guess whose eyes were glued to the screen?
In the A Certain Magical Index light novels, Brunhild Eiktobel puts to sleep a little boy she's been watching over when she senses danger. The last thing she needed was for the boy to see the ensuing carnage when her attackers struck.
Mizore casually covers Yukari's eyes in Rosario + Vampire Capu2 after Ruby trips and exposes herself, while a confused Yukari tries to look around her hand.
An inversion happens in the chapter "The Most Bizarre Bizarro Of All" from the Bizarro Comics anthology. When a Bizarro starts walking on his hands and generally acting even too strange by Bizarro standards, all the children tell the adults not to watch or listen. (It is Bizarro World, after all.)
In chapter 33 of Magical Troubleshooting Crossover Fighting Federation UltrasuccubusMorrigan strips herself naked in an attempt to distract Wolverine during a match. Combat CommentatorHiroshi covers guest commentator Sana's eyes, which she protests, since she has the same basic anatomy as Morrigan.
In the 1994 remake of Angels in the Outfield, Roger covers up JP's ears when George Knox starts swearing during the game.
In Spy Kids, the parents ask the kids to shut their eyes before beating up a bunch of Mooks.
In Hot Fuzz, Nicholas covers a child bystander's eyes when one of the bad guys impales himself on a model building.
In Charlie and the Chocolate Factory, after Mike says "I hate chocolate," Grampa George begins to rant, "Well it's a good thing you're going to a chocolate factory, you ungrateful little-" At which point Charlie's ears are covered by Mr. Bucket, and we hear nothing until he removes them. Fair guess that it's swearing.
In The War of the Worlds, Ray Ferrier blindfolds his daughter and tells her to cover her ears and sing her calming song so she won't see or hear as he kills Ogilvy.
Used in the movie Old School, where Vince Vaughn's character sets up a system where he tells his child "earmuffs," and the kid will cover his ears, allowing adults to say what they will.
In Friends, Ross walks in with his son Ben just as Phoebe starts cussing out a game machine. He immediately dives to cover Ben's ears before shouting "Phoebe!" to get her attention and make her stop.
There's a House episode where the mother of a preteen girl covers her daughter's ears so she won't hear the word "masturbation".
An episode of Get Smart had Max communicating with a trapped Chief via Morse code. After Max bungles his rescue, Chief sends out some angry sounding taps. Max responds with "Watch your language, Chief. There is a lady present." When the angry taps continue, Max covers 99's ears.
In an episode of Bones while discussing the case of the week in front of Booth's young son, Booth covers his son's ears and makes him sing a little song while the adults talk.
In Ugly Betty Justin is repeatedly told to put his headphones on during the second episode, when he is still rather young.
A post-9/11 Blondie strip parodied the, um, excesses in airline security by having Dagwood have to repeatedly go through a metal detector, with the operator making him take off more clothes each time. He's in his underwear and the machine is still beeping when another guard comes up and tells the operator that the machine's broken. Cut to Dagwood on the plane begging the flight attendant to let him put his clothes back on before take-off, with a mother covering her kid's eyes elsewhere in the panel.
If Jack, known for her unusually foul mouth in Mass Effect 2, survived that game's endgame, in 3 she turns up as a teacher and makes a special effort not to swear in front of her students. Joker teases her that her Swear Jar could fund the war effort by itself. At which point Jack tells the kids to cover their ears and the scene cuts away.
In Yamara, a dark elf mother covers her son's eyes when the tour they're on visits an erotically-carved temple. Ironically, the tour members had already been tortured as part of their visit, but the boy's mom doesn't mind that, only the raunchy art.
In SpongeBob SquarePants, Spongebob indulges in some Innocent Swearing over the PA system of the Krusty Krab. Among the shocked customers, one octopus mother uses her arms to cover up her children's ears, and manages the fifth by sticking a popcorn bucket over his head.
Ned Flanders does this to one of his sons in an episode of The Simpsons after Moe loses his temper and repeatedly uses the word "freakin'". The boy cries "Ow, my freakin' ears!"
A variation where Bart is sent to a religious school and is asked by the teacher to recite a poem. Bart complies with "Beans, beans the magical fruit! The more you eat the more, you toot!" Cut to Bart fleeing the furious mob, with the teacher yelling "Avert your eyes, children! It may take on other forms!"
This happens in Family Guy at one point. Peter takes Stewie to the bar with him, and Quagmire is about to tell a story of what he did with some women last night. Peter covers Stewie's ears so he won't hear and we see some very strange pantomime on Quagmire's part but hear none of it thanks to Peter.
In The Boondocks, Sarah covers Jazmine's ears when Tom starts swearing after the basketball team he is coaching not only loses but he misses the opportunity to have a "miracle" win.
In one scene from Little Miss Sunshine, the adults in the van were having an obscenity-filled conversation while young Olive listened to music on her headphones. The director made sure that nine-year-old Abigail Breslin, who played Olive, had the music on her headphones loud enough that she actually couldn't hear the conversation.
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