A federal monarchy is a federation of states with a single monarch as over-all head of the federation, but retaining different monarchs, or a non-monarchical system of government, in the various states joined to the federation.
The term was introduced into English political and historical discourse by Edward Augustus Freeman, in his History of Federal Government (1863). Freeman himself thought a federal monarchy only possible in the abstract.
The concept played a role in political debates in Italy and Austria-Hungary in the nineteenth century and in Yugoslavia in the twentieth century, but it was not put into effect in any of the cases. For example, modern Italy had not unified until Risorgimento of the late 19th century, with its land still being divided into several smaller kingdoms, duchies, republics, etc. each headed by a different dynasty or ruling class.