The Nintendo Network credit card charge applies to children aged twelve or under.
In an effort to keep itself current with US child protection legislation, Nintendo is charging $0.50 when parents request access for their child on the Nintendo Network. The fee is only charged once, and after that as many kids as the parent chooses can be set up on the system; the Parental Control PIN is all that's needed.
The credit card charge is to keep Nintendo compliant with the Children's Online Privacy Protection Act (1998), aka COPPA, which is aimed at businesses that market to children and collect their data online. The fee only applies to parents setting up accounts for children under the age of 12. Nintendo promises that the credit card info isn't stored on the Wii U, and can't be used by cunning kids to drain the parent's credit. For more information, see here.
Of course, tricks like these can only work so long as kids don't have cards of their own, a situation that may not last that much longer. In the meantime, parents should get their cards out; Nintendo Network isn't precisely free, but $0.50 shouldn't strain your budget.
Source: Game Informer