The term 'monopoly on violence' refers to the idea that within a certain
jurisdiction, only one organisation has the power to commit violent acts legitimately.
Practically, in most countries in the world, the state or government is the organisation which creates laws, and uses a monopoly on violence to enforce those laws.
For example, in Australia, any violence between citizens is regarded as illegitimate, whereas violence by a body representing the state (such as the police or the army), is seen as legitimate until proven otherwise.
The term 'monopoly on violence' has been used by various sociologists throughout history, for example Karl Marx and Max Weber.
Legal systems do exist which do no include a monopoly on violence, however. The system known as anarchism incorporates such a concept.