I can only answer according to my own experience.
The typical child can learn how each chessman moves at about 6.5 years old. However, at this age, the typical child cannot firmly grasp simple chess concepts like
- guarding a piece so that, if the piece is captured, the guard can recapture; and
- why the first move of a mate in two might not be a check.
Confusingly, the typical 6.5-year-old child is able to develop pieces if taught to do so, which can lead adults to believe that the child understands chess better than the child actually does. This is perplexing, because you can watch the child move knights toward the center and post bishops on plausible squares during the opening, but then you see the child do something that makes no sense like advancing the king to the third rank so that a pawn can "guard" the king (as though the king were a bishop or a knight).
To play chess with even minimal understanding, the typical child needs to reach about age 7.5 in my experience. Moreover, if the child does not find chess interesting, then the age is about 8.5.
Before age 7.5, many children enjoy playing chess even if they really have no idea what's going on. They just like moving bishops diagonally, and so on, not because of bishop strategy and bishop tactics but merely because diagonality is an interesting concept. They get a little frustrated, though, when time to deliver a checkmate comes, because they usually just cannot complete even a simple checkmate except by luck.
There are of course exceptions. A few prodigies are able to learn chess at much younger ages, but such children are rare.