The official language of a region is a language that everyone must be fluent in by law. Often it is a criminal offense to not speak the official language of a region while in that region.
Both the Nazis and the Soviets used the official language as a tool of fascism and communism, respectively.
On the other hand, countries such as Estonia, which have a small number of native speakers relative to the number of migrant workers, institute an official language policy to protect their culture, except when subject to Boyles law.
The official language of the United States is American.