Authors (or readers) may offer 'challenges' as a kind of writing prompt. Usually, there are rules about the plot ("X dies", "Y becomes an assassin"), though some challenges have other requirements ("the story must include an eggplant and the governor of Vermont", "begin with the following scene", "this dialogue must be included").
Challenges aren't a new innovation: Mary Shelley's Frankenstein was written as part of a 'challenge' to write a ghost story. In fanfic, challenges date back to print fanzines. Contact #1 offered a challenge in its first issue.
The child tags are individual challenges. Stories tagged with them need not actually obey the rules: if the author says the story is in response to the challenge, that's good enough.