A Council of Magic is a governing body of the wizarding community in some countries. Headed by a President, a Council of Magic is, most likely, responsible for regulating and enforcing laws for the magical community, as well as keeping said community hidden from the Muggle world, as is a Ministry of Magic.
Known countries with Councils of Magic
Behind the scenes
- The Argentinian Council of Magic is the first magical government in the series not to be referred to as a "Ministry of Magic". It is unknown precisely what distinguishes a Council of Magic from a Ministry of Magic, but a possible explanation would be that while a Ministry is answerable (nominally, at least) to the Muggle cabinet, the name "Council of Magic" implies no such thing.
- Pottermore (Mentioned only)