A kid and his parents are on a camping trip. Happens all the time in real life, nothing unusual here. But the kid decides to explore a little bit, and before he knows it, he's lost. Or a bear shows up and threatens the family, and the kid ends up separated from the parents. Or whatever happens... basically, the kid ends up separated from the adults. And ends up going on his own adventure, naturally.
This happens all the time in kids' stories. It's one thing to have a Kid Hero who runs around the place, encounters criminals, and stops them singlehandedly, but that's not very convincing. And having a kid and the parents go on an adventure and get into danger at the same time often isn't as fun as having the kid go on solo adventures. By separating the kid(s) from the adult(s), you have a more convincing, "realistic" reason for the kid to be alone while getting into trouble or danger.
As such, this is how lots of adventures start, or how they escalate.
- Spirited Away. First thing that happens is the parents go and do something dumb, so Chihiro's on her own.
- Home Alone, as the title itself suggests.
- Aliens in the Attic enforces this by the alien mind control device being unable to affect anyone underage.
- In Doc Wilde, when one of the adults becomes possessed and wanders from the camp, Doc's son is the only one to witness it, and tries to follow him, leaving him separated from the rest of the group.
- The Candy Shop War involves every single adult being controlled by white fudge, making them essentially zombies, thus making the kids "mentally" separated from the adults rather than physically. As a result, they are no help at all when the heroes request help. Or get attacked by wooden Indians.
- Allana/Amelia Solo does this intentionally quite often.
- Happened an awful lot to her dad and his siblings when they were little, too.
- Almost constantly in Galaxy of Fear. In the first several books the Arrandas and their uncle Hoole are wary of each other and distant. He doesn't like spending much time around them and has a lot of mysterious errands to go on, instead leaving them with his droid assistant DV-9. Later in the series Hoole and the Arrandas are on much better terms and DV-9 is Put on a Bus. They still end up apart fairly often, and a main general plot of the series is once lampshaded by Hoole.
"This is a pleasure. I have left you alone for several hours, and nothing eventful has happened. No Imperial invasions. No dangerous criminals."
- An American Tail: Fievel is separated from his family on their way to America, and again in the sequel on the way to the West.
- The Land Before Time: Each of the child characters are separated from their parents and guardians on their way to The Great Valley.
- Finding Nemo: Sort of an inversion, since it's the adult that has to go on the grand adventure to find his son. Not that Nemo doesn't have an adventure of his own.
- Jonny Quest (1960s version). In "Monster in the Monastery", "Werewolf of the Timberland" and "Attack of the Tree People", Jonny and Hadji are separated from Race Bannon and Dr. Quest for an extended period.