A more thorough explanation:

Child-benefit theory is a principle that allows state funds to be provided to private-school pupils if the allotment can be justified as benefiting the child. This theory is also known as student-benefit theory.

For example, the Supreme Court upheld a Louisiana law that allowed the purchase of textbooks for all children throughout the state, including those in private schools, under this theory. This means that if the state can prove that providing textbooks to private-school pupils benefits the child, then it is allowed to use state funds to do so.

Another example of child-benefit theory is providing transportation services to private-school pupils if it can be justified as benefiting the child. For instance, if a private school is located in an area where public transportation is not available, the state may provide transportation services to ensure that the child can attend school.

Overall, child-benefit theory allows the state to use public funds to benefit private-school pupils if it can be justified as benefiting the child.