Pre-teens and young teens in fiction will wander about their town, ride their bikes around the region, or even explore the countryside, with little adult supervision or even concern. They'll ride down to their friend's house on the other side of town and go outside at night to places on the outskirts of town to explore old houses and vacant lots. In some stories, pre-teens may go on trips across the country without their parents.
In the U.S., it was in the mid-Eighties when media-promoted fears of kidnapping and strangers ("Stranger Danger"), which caused parents and society to clamp down on the freedom of children to wander unsupervised.note Before then, kids were commonly allowed much more latitude, particularly in the summer months, concerning what they did and where they went, whether in a city or in the countryside. City kids were allowed to play games in vacant lots and explore local streets. Kids in the countryside could bike all around their small town. While the freedom kids had to run about town still wasn't necessarily as great as it tends to be in fiction (at least some parents still needed to know where they were going, when they were going to be back, etc.), they were often allowed to at least take their bikes to local shopping centers, swimming pools, libraries, or woods. This was the particular case in a Close-Knit Community where other adults would notice and intervene in cases of danger. Generally speaking, in such places, a child was at least old enough to have independence and given safe parameters to stay within; in fact they usually had some sort of supervision from being in a group, with older kids, or by trusted adults passing by.
Unusual travel permissiveness in a story can be an acceptable break from reality. A show involving little Timmy and Sally being driven everywhere by their parents wouldn't be very exciting. Parents are, after all, useless and boring, and the kids wouldn't be able to explore that Abandoned Warehouse and solve mysteries, and have grumpy adults yell "You Meddling Kids" at them.
It's important to note, that despite the above-mentioned overreaction in the United States, it is not entirely without merit that people shifted away from this in real life and even in fiction. Even back in the 20th century, there was always a degree of precaution when allowing kids freedom. Children would normally be let within age-apprioate boundaries. (such as a six-year-old walking to a nearby school or park, maybe in a group) Even in close-knit communities or places like Japan, a toddler would typically not be left alone to wander without supervision even at the age of three or four (once out of diapers); communities across the world typically had some sort of precautions in place to ensure children's safety, though is varied how. Parents who did not overreact to the publicized kidnapper simply became more aware of the inherent risks of giving a kid too young more freedom than they should, as younger kids do not yet have the full cognitive ability or capacity to make rational life decisions when left to their own devices.
In fact, this trope has actually led to consequences such as injury and even death in extreme cases, often do to negligence on the parents' or caretakers' parts. How much merit this has is contextual and depends on a variety of factors such as: the age of the child, maturity, time, location, and infrastructure of the area.
Additionally, there were still numerous problems with parents being too permissive and letting kids too young wander in to dangerous locations such as construction sites, city streets, and (depending on the areas) woods unattended. sometimes at night. Other times kids commonly did not even see their parents for much of the day, and were kicked out of the house (usually until dinner) just so the parents did not have to put up with them, leading to cases of neglect and various emotional and behavioral issues later in life, as well as kids (at times) getting injured or preyed on by bullies. It is also worth noting that, while rare, it did not mean stuff like kidnappings and molesters preying on kids never happened at all.
There is no blanket answer to this trope, in real life or fiction.
Compare Minor Living Alone and Invisible Parents for one of the more notable examples of this trope at work and Free-Range Pets for the animal equivalent. See also Kids Driving Cars, which takes this trope to the extreme. One extreme can be the Missing Child. Another extreme can be outright Parental Neglect if this trope is taken too far or outside of reason.