Official English refers to proposals to designate the English language the official language of the United States. The United States currently does not have an official language although English is the de facto common language in the U.S.
The correct name of the movement is Official English. The term, "English-only" is used by opponents of the movement and left-wing academics to denigrate the Official English movement. "English-only" is factually incorrect, because the goal of the movement is to make English the official language for government functions in the United States, not to ban the private use and study of foreign languages. An essay on the ProEnglish website explains the distinction between "Official English" and "English-only", and why Official English is the proper term.
In the United States the three main groups promoting Official English are U.S. English, ProEnglish, and the smaller group English First.