This idiom means that children had to take on responsibilities that were typically expected of adults. In this case, the children had to gather wood for the family to use for cooking and heating. This would have been a difficult and time-consuming task, but it was necessary for the family's survival.
This idiom can be used to describe any situation where children are forced to take on adult responsibilities. For example, you might say this about a child who has to take care of their younger siblings while their parents are at work.