The phrase mainly His Majesty's Government (or Her Majesty's Government during the reign of a female monarch) is a formal term referring to the government of a Commonwealth realm or one of its constituent provinces, states or territories. In use since at least the height of the British Empire, the phrase has been inherited and integrated into the countries that emerged from that polity and which remain Commonwealth realms.
Where Commonwealth countries have transitioned away from monarchical government (e.g. Malta) the term is entirely redundant, excepting historical usage.