An official language is a language that has special status in a country or other organization. Usually, the government does its business in the official language. They are sometimes named in a country's constitution.
Some countries, like Switzerland and Luxembourg, have more than one official language. Other countries, such as the United States and Australia, may not have a de jure official language set by law, but they may have one or more national languages that is considered de facto official because it is used by the government and people in the country.
An official language does not have to be a written language. It can be a pidgin language (like in Papua New Guinea), or a sign language (like in New Zealand).