Most people would probably define government as an agency that provides certain services (such as defense), a body of rules and the enforcement of this body of rules within a defined territory.
Providing services and rules (including their enforcement), i.e. providing governance is certainly what the government does – but many agencies in society other than government do the same.
A golf club, for example, provides certain services (the infrastructure necessary for playing golf), a body of rules (for example, a certain dress code its members are obliged to follow) and the enforcement of this body of rules (repeated violation of the club rules may, for example, lead to exclusion from the club).
Since there exist countless governance providers other than government, the definition of government provided above is obviously not sufficient.
The difference between government on the one hand and other governance providers on the other is that the governance provided by non-government governance providers has been voluntarily chosen and explicitly consented to.
And this fact makes all the difference.
When somebody slices open my stomach, this is usually considered assault. But if I have voluntarily chosen to sign a contract explicitly consenting to a surgical procedure to remove a tumor from my stomach, the surgeon does not violate my rights when cutting me open.
The absence of consent to the government means that the acts done by government would be considered a violation of individual rights, if done by private agents.
For example, when person A does not consent to a transfer of money from himself/herself to person B, this is called robbery – and person B is regarded as a robber.
Taxation by the government is, in principle, no different from the act of the thief. The taxpayer has not consented – and may even have explicitly objected – to the transfer of money to the government.
True, the government provides taxpayers with services in exchange for their taxes – but it insists on collecting the taxes whether or not a taxpayer wants the services. So extortion rather than robbery might be a more appropriate description of what the government is doing. Either way, if it were the act of a private party, everyone would agree that it was a crime.
The definition of government that follows from the foregoing is this:
Government is a governance provider that has not been voluntarily chosen (consented to) by those subject to its governance.