The exclusive ability of a sovereign nation to control violence in order to enforce the law and maintain security. Ironically, a government does this by wielding the most force to back up its words.
The police kicked down the crack house door and served a search warrant after detaining the residents at gunpoint.
"That is what essentially sets a nation-state apart, which is the monopoly on violence." - President Obama
Soldiers are authorized to kill during war. Normally this is the highly illegal act of murder.