This is likely not possible with current tech ( considering most places still don't even let you pay with your cellphone) but my idea is that the app would allow parents to approve specific purchases for their kids or teens.
For example let's say a 13 year old wants to ask their parents for money to buy some food while at the mall with friends, they decide what they want to buy and when they go to pay for it with their smartphone the app sends the parent the receipt/bill electronically over the app.
The parent can then choose to approve or deny the payment. If they approve it then the food (or any other items) are paid for and the purchase is complete. If they deny it then the kid or teen either has to use their own money to pay or they cannot buy the item(s).
Obviously this would not work at food places where they make the food before you pay, unless maybe they ask how you are paying before you order, but it would work in a lot of other cases like with clothes or packaged food, and of course places where you pay before they make your meal.
This is better than parents simply giving their kids cash because they know exactly what they are buying and that the money is not being wasted on things they don't need like overpriced clothes/jewelry or even drugs. I'm sure there have been plenty of cases of kids saying they want money for say the movies and using it on something Illegal/wasteful/possibly dangerous.
It would also allow parents to have a log of what they/their kids have bought recently and how much they spent. I think after kids got used to using the app to ask for money they would know to text their parents and ask before they try to buy something.
While the main use is for kids/teens, the app could also be used by parents who want to support their young adult child (say by buying their groceries/gas for them) but not allow them to waste a ton of their parents money on things they really don't need like tobacco, alcohol, or other junk.