Max Weber's definition of the state as a human community that successfully claims the monopoly of the legitimate use of physical force within a given territory.
In more detail
Weber gave the definition in 'Politics as a Vocation' (1919). It defines the state by its means rather than its purposes, and emphasises legitimacy: other actors may use force only with the state's permission. The concept is used to analyse state capacity, failed states and private or non-state armed actors. Critics note that many states never achieved such a monopoly and that private security, militias and transnational actors complicate it.