Normally a government monopolizes force within a sovereign country.
The effectiveness of a government is how much other (non government) force exists in that realm. For instance, a powerful Mafia undermines the government because they use force to achieve their own aims which are generally contrary to the governments aims (though in some cases they have a close relationship too).
Statements like 'The government's role is to serve the welfare of the people' are naive and misguided. These may (or may not) be good things a government can do, and it may be the justification used by those who want to lead government, but it is not fundamentally what government is.
Historically, as social sophistication and technology increased, so too did the size of social groups. This led to the ability of power blocs to control larger and larger populations. A government of a large country can control a population unimaginable to a tribal chief.
At the start of the 21st century there are two main government models.
All governments interfere unnecessarily in the lives and the businesses of their populations.
This work takes the view that the only legitimate function of government is to minimize initiation of force (ie to maximize freedom).