The etymology of the word Intimation comes from the Latin “Intimatĭo” which means to intimate, which is a verb, therefore it is the action and effect of intimacy. The fact that a person takes the action of intimacy to another could be taken as a kind of threat or warning, that whether or not he does something that she asks him, he would or would not take some kind of retaliation against him.
The fact of intimate someone means that the fulfillment of a request is being demanded but with the effect of authority or force, so that they are obliged to fulfill it. For this reason, it is implicitly felt that some kind of ultimatum is hidden in the intimation, in case what is being requested or demanded is not fulfilled, they will be forced to take actions (which may be some type of punishment).
The act of intimacy is a power that is generally attributed to those with legal power or authority; One of the types of intimation that they can exercise is a payment request, which is a notice that is generally sent in writing and where a deadline is expressed, to demand the payment of a service, product or tax, of not making payment on that deadline date, measures will be taken against you (it may be that the service provided is suspended, or that a lawsuit is opened, among others).
Other ways in which the authorities can intimidate the population is by demanding public order, an example of this, requesting the delivery of weapons to those who do not have permission to possess them, or demanding not to circulate on the streets when there is a curfew, etc..