The term administration, as used in the context of government, differs according to the jurisdiction under which it operates.
[1] In American usage, the term generally refers to the executive branch under a specific president (or governor, mayor, or other local executives); or the term of a particular executive; for example: "President Y's administration" or "Secretary of Defense X during President Y's administration.
The term "administration" has been used to denote the executive branch in presidential systems of government.
Still, most typically the word "administration" refers to managerial functions in general, which may include local governments, or the hierarchy of national and local government, that applies to a town or district.
An older, chiefly Commonwealth usage, is the term "ministry", as in "Churchill Ministry", which is still in official and academic use in Britain, Australia, and Canada to refer the terms of prime ministers.