Or, they may want to live a childhood they never had.
One can roleplay a child or teen of the opposite sex, or from a different time period (the old-time schoolhouse, or being a child in the Roman Empire), or even a scenario that's totally made up (being a teenager in a world in which it's perfectly acceptable for parents to punish unruly teens with, say, bondage).
We fold in elements from the lives of children we see around us, in real life or in movies, TV shows or books, and from our own imaginations.
The roles ageplayers want to play may bear little or no resemblance to their real childhoods, by accident or by design.
There are a few elements commonly seen in ageplay: clothes and costumes are one, from little frilly baby dresses, footed PJs and snap-crotch Oshkosh overalls to school uniforms and whatever wacky fashions are popular among those crazy kids today.
Microwave ovens and other modern conveniences have changed our lives profoundly just in the past decade or two. Usually you need at least two people for this, and often one will play the "child" role and the other will play an adult caregiver of some kind (mother, father, other relative, babysitter, nanny, etc.).
When we think back, there are certain memorable moments we can remember well, good or bad, but the unremarkable everyday events have blurred together or maybe even disappeared.
When we try to remember what's in the gaps between those memorable moments, what we usually end up doing is reconstructing the past based on those vague blurs and sharp moments, and of course we're doing this from adult vantage points, so there is a lot of other information that gets mixed in.
And, of course, there is infantilism, where one player is the baby and the other is the caregiver.
But these are just some commonly heard-of examples; people are very creative and come up with many more ideas.