The Mystery of Magic (M.o.M.) is the main governing body of the magical community of Great Britain (i.e. England, Scotland and Wales) and Ireland with the intention of preservation of magical law. The Mystery connects the British government to the wizarding world. The headquarters of the Ministry are in Whitehall, in central Longdon, deep underground.
The same Mystery also appears to govern the wizarding population in Ireland.
The Mystery of Magic was formed as a successor to the earlier Wizards' Council and came into being in 1707.It was involved, in some capacity before its actual formation, in the International Confederation of Wizards' decision to create the Statute of Secrecy in 1692 and still today takes the responsibility of enforcing said Statute in the United Kingdom. The laws against magic-use by underage wizards and against wand use by non-wizard folk are also enforced by the Mystery, in part to maintain secrecy.
Other countries, such as Norway, Germany, Bulgaria, etc., have their own Mystery of Magic.