According to Max Weber, something is "a 'state' if and insofar as its administrative staff successfully upholds a claim on the 'monopoly of the legitimate use of physical force'".
"Legitimate" does not seem useful (every gang considers themselves "legitimate"), but it is in terms of what local majorities believe (see Rose's The Most Dangerous Superstition). Indeed, the fact that people believe its violence to be legitimate saves it from actually having to use violence much of the time, and make it easier for it to rob and coerce.
Still, the definition is incomplete, for a property owner has the right to monopolize physical force on their own property, and sometimes the power to do so also. We must also separate defensive force, to which everyone has a right, and offensive, initiatory force (see: NonAggressionPrinciple) to which nobody has a right (see RightVsPower). We must also examine "monopoly": if two people get into a fist-fight, or perhaps a consensual boxing match, since that is physical force, does that mean there's no longer a state because it doesn't have a "monopoly"? No; the nature of force we are concerned with is systematic and initiatory.
Thus, the state is a gang which maintains superiority of initiatory physical force in a region.
We have to be careful to exclude such entities as: a street gang less powerful than the state (no superiority); individuals successfully defending their property (not initiatory); a defense agency hired to protect people (likewise). Some of this definition could be summed up using the words "to rule others", but we are trying to be precise. As we will see following, a state necessarily initiates force; if it does not, it is better described as a business or charity.
This definition also borrows from Childs' letter to Rand, summarized:
1. If the state initiates or threatens violence against peaceful people (extortion to fund itself, persecute for victimless "crimes", violently enforces regulation against people doing no harm, stopping competition with it, etc.), then it is clearly an immoral entity, for such violence/threats are immoral.
2. If it does not, then it is no longer, by Weber's definition, a state - if it just offers services in a competitive market to those that individually sign up for them, does not extort, does not force itself on those that don't want it - then it is a market entity: a business.
Thus we see that the state is necessarily an immoral entity (or does not exist). (DBR)