(A) What is a government?
The word "government" is defined by the oxford English dictionary like: “the group of people with the authority to govern a country or state; a particular ministry in office”.
A government is a very useful tool for organize the human society, because we need an orden system that manages all the efforts of the same for their own benefit and prosperity.
The origin of the government lies in the State. In the beginnings, the human’s societies were small and were governed by the law of the stronger. If you could protect your properties, or even rob other, which would be fine because that was the normative. This is the state of nature, or what we call "Natural Law", where people organize themselves around self-sufficiency and self-interest, as well as self-survival.
But, when the societies grew, became intolerable this type of behaviors. In a scenario where there is a government, people are organized in a society with rules or laws which govern their conduct.
The state was created to protect the physical and material integrity of the members of a society.

(B) Utility and functions of a government organized.
In the human history, have existed many types of government, and some have been better than others, regarding the division of property and justice among different social strata comprising citizens who form the state, but all have been "organized" in one way or another.
From my perspective, an organized government works as a social regulator, handing territories, resources, responsibilities and justice among the citizens who make up the State, regardless of whether how the government was formed (Monarchy, Republic, etc.)

(C) Government in U.K.
There are different levels of government, but the national government is made up of Members of Parliament (MPs) who sit in the House of Commons and are democratically elected. The Prime