You're watching your favorite adventure series. A group of plucky kids snoop around the place, get into exciting situations, and even get into danger and need to be rescued. And in the end, a cop arrests the criminal the kids were after. Supposedly, the kids didn't even help the police at all.
Suddenly it dawns on you. The main characters aren't that useful! They did all the cool stuff (basically, get into all the danger), yet someone else ultimately stopped the bad guy and saved the day. What the heck? Why even bother with these "heroes" and their adventures?
Because this is a story where the main attraction, if not the very point, is to watch ordinary people get into all sorts of excitement and danger. Yet they can't ultimately thwart the villain or solve the problem, because, well, that's not their job, nor do they have the actual skills for it.
This is a way to get kid characters (or average, non-professional adult characters) into an exciting adventure while providing the realism of showing the real police or other professionals doing their jobs and saving the day. Note that despite the title, this doesn't have to be about young characters specifically; this is about when the main characters, regardless of who they are, are not the ones who save the day (though Character Developmentdoes happen).
See also Little Hero, Big War, which is kind of this on a much larger scale, and with the hero having a larger chance of being the one who actually defeats the villain.
In The 13th Warrior, main character Ahmed Ibn Fahdlan is a useful extra swordsman but doesn't actually do anything to resolve the plot, with the single exception of figuring out how the group can escape from the Wendol cave. Of course, since the story is really about Bulliwye/Beowulf, this is understandable.
Ahmed also figured-out that the Wendol liked to act, and maybe even think of themselves as bears, and this allowed the group to find the Wendol cave to begin with. However, he was mostly an audience identification character and eventual chronicler of Bulliwye/Beowulf, so he still fits the trope well.
In Goldfinger, the role of James Bond in the plot is actually rather limited. He spends most of his time tailing Goldfinger and hanging out in his base as a prisoner, always trying to get intel outside, but failing. Sure, he does manage to kill both Goldfinger and Oddjob, but that doesn't affect the plot very much, and the bulk of the work ends up being done by the US Army and the CIA. They even disarm the nuke for Bond. The only vital thing Bond does manage to do is, ironically enough, screwing Pussy Galore (who then performs a Heel-Face Turn and sabotages Goldfinger's 'grand slam').
Guards! Guards! has the Watch figure out who the Supreme Grand Master is, but it is implied that Vetinari was already aware of what was going on, and the Watch are ultimately useless in getting rid of the Dragon - Errol ends up defeating it by creating a sonic boom, which was part of his mating dance to the female dragon.
In the Left Behind books, the main characters, calling themselves the Tribulation Force, basically sit around and try to survive the tribulation, but do nothing that actually affects the events of the story in any way. The books could basically be described as a travelog for The End of the World as We Know It.
In the original, 1920s Hardy Boys stories, Frank and Joe's "investigation" often ended up with them hiding in a corner or tied up by the villains until their father and the police force arrived to save the day. This was eventually changed in the later books to make them more useful.
Similar to the above example, in Janie's Private Eyes, the fourth book in The Stanley Family series, while 13-year-old David, 8-year-old Janie and 6-year-old Blair actually do solve the case, they end up in danger and have to be rescued. Fortunately, someone else calls the police and rescues the kids, resulting in the police solving the case without the help of the kids' hard work.
Despite having the most screen-time in Good Omens, Noble Demon Crowley and the pragmatic angel Aziraphale have no effect on the main events of the story, though not for a lack of trying. Arguably though, having Armageddon be averted by humans only, without angelic or diabolical help was the whole point.
Really, most of the rather large cast is like this—the final battle pretty much comes down to the Them vs. the Horsepeople. Shadwell, Madame Tracy, Anathema, Newton, and Ligur all turn out to be pretty pointless, not even counting other characters who had died/disappeared from the plot by this point. (Admittedly Newt's presence might have contributed, it's kind of unclear if the Horsepeople's defeat stopped the nukes or just made it possible for him to.)
Generally averted in the A-to-Z Mysteries series, but played straight in the book The Canary Caper. This story revolves around a series of pet kidnappings ultimately solved by the police. Even when the three main kids discover a pattern in the kidnappings, Officer Fallon says they already made the connection. The kids hide outside the thief's next victim, but the police show up before they can even catch the petnapper.
Ishmael, in Moby-Dick. The only thing that really distinguishes him as a character is that he's the only member of the Pequod's crew not to die.
Invoked and justified in a few episodes of Doctor Who.
Certain events, especially those based on Real Life history, require the Doctor and his companions to be this trope while otherwise solving the problems connected to what the show calls "fixed points in time" (the event must take place within a rigid set of circumstances defining the end result or reality will collapse). A good example is the Tenth Doctor episode "The Fires of Pompeii", where the Doctor and his companion discover alien beings called the Pyroviles are using Mount Vesuvius to stay alive, and to prevent the danger they pose humanity, Vesuvius must erupt as history dictates, leaving the protagonists unable to stop the historical event. They are, however, allowed to save at least one family of people from the event, since history doesn't record anything that would contradict their survival.
This also happened in "Warriors' Gate" (where it was intended to be An Aesop about "doing nothing" sometimes being wiser than pointless action), and in certain stories during Eric Saward's tenure as script editor (where it was probably because of Saward's belief that the Doctor just wasn't as cool as his own Badass military characters).
In "The Time of the Doctor" the Doctor explains his default plan: talk a lot, hope something good happens, take the credit.
The Venture Bros., who were based on the Hardy Boys and Jonny Quest both, really did nothing in the show during the first season, but are the main characters nonetheless. This changed in later seasons.
In the original 1960s series, Jonny Quest basically just hung around while his dad and Race dealt with all the dangerous stuff. Ocassionally, he, Hadji and Bandit would need rescuing, and would even take down a mook or two, but otherwise did little but comment on the action.
This was realized when Jonny Quest: The Real Adventures was made, resulting in the younger cast members being much more capable of fighting and getting out of trouble, not to mention being aged up a bit.
Scooby-Doo's Scooby Gang, the meddling kids themselves, are an odd case, as they actually do manage to solve mysteries... or rather, Velma does, with a little help from Freddy and occasionally Daphne. Our main heroes, Scooby and Shaggy, on the other hand, mostly just have exciting chase scenes and eat lots, while Daphne is kidnapped by the villain ("Danger-prone Daphne", indeed) and Freddy makes traps that invariably fail but somehow manage to accidentally capture the villain anyway. In the end, it's Velma who figures out who the villain is and explains the mystery to the others.
To be fair to Scooby and Shaggy, their chase scenes sometimes involved them being chased by the villain right into Fred's trap, inadvertently capturing the bad guy. Shaggy himself is the Trope Namer for the Shaggy Search Technique, and is often the one who finds the clues to the cases.
This is averted hilariously in the movies, in which the cast also realize their shortcomings - Daphne takes down a good number of bad guys after taking martial arts classes and Shaggy and Scooby spend the entire second movie performing investigations on their own to prove their worth (of course, the success of said investigations is pretty limited...)
The third live-action film averts this. Every member of the gang provides something useful, but not at the same degree as the earlier two films (which is correct, as this film is a prequel). Freddy comes up with the plan, Daphne provides the wheels and disguises, Velma provides science and history, Shaggy drives and provides a list of suspects (and the motive), and Scooby actually catches the villain.
The third episode of the original series is a perfect example of this trope. The police would have caught the criminal even if Mystery Inc. had not ended up in the castle.
In "A Clue for Scooby Doo", "Bedlam At The Big Top", and "Never Ape an Ape Man", Scooby and Shaggy do have a major role in solving the case.
For "A Clue for Scooby-Doo", Scooby-Doo finds the air tanks for the gang while Shaggy sits on the rock that opens up the villian's hideout.
For "Bedlam At The Big Top", Shaggy and Scooby-Doo put the Ghost Clown into a trance in which the Ghost Clown thinks he's a chimp.
For "Never Ape An Ape Man", Shaggy takes a picture of the Ape Man without his mask on. Talk about carrying the Idiot Ball, Carl The Stunt Man.
Not to mention in many later spin offs where Velma and Fred were absent, leaving Shaggy and Scooby to use Bugs Bunny style antics to take down the Monster of the Week (who were often real this time).
Shaggy is quite often shown to be considerably smarter than he looks. He and Scooby are perfectly capable of solving a mystery on their own, if they have no choice but to focus on it. He was also the first one to recognize the unmasked Capt. Cutler.
Captain Planet and the Planeteers is sort of like this. The Planeteers are the real main characters, with Captain Planet himself usually only getting about two minutes of screen time per episode. He is, however, the Deus ex Machina that solves all the major problems, while the heroes are mostly there to just summon him and learn the Aesop (green or otherwise) du jour, after getting into a lot of danger and adventurous situations, of course.
The children in The Amazing Chan and the Chan Clan try their hardest, and are usually the ones who get the ball rolling, but it's always their dad who ends up solving the mystery in the end.