A more thorough explanation:

Definition: Local-law theory is a concept in conflict of laws. It suggests that even though a court recognizes and enforces a local right (a right created under its own law), in a foreign case, it does not necessarily apply the rule that would govern a similar case of a purely domestic nature. Instead, it considers the law of the foreign country and creates a local right that is as close as possible to the law of the country where the decisive facts have occurred.

Example: Let's say a person from the United States is involved in a car accident while on vacation in France. The person sues the other driver for damages in a U.S. court. The court will apply the local-law theory and consider the law of France, where the accident occurred, to determine the extent of damages. The court will create a local right that is as close as possible to the law of France.

This example illustrates how the local-law theory works in a foreign case. The court does not apply the law of the forum (the U.S. in this case) but instead considers the law of the foreign country (France) to create a local right that is as close as possible to the law of France.