Imperium is a Latin

Latin

Latin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...

 word which, in a broad sense, translates roughly as 'power to command'. In ancient Rome

Ancient Rome

Ancient Rome was a thriving civilization that grew on the Italian Peninsula as early as the 8th century BC. Located along the Mediterranean Sea and centered on the city of Rome, it expanded to one of the largest empires in the ancient world....

, different kinds of power or authority

Authority

The word Authority is derived mainly from the Latin word auctoritas, meaning invention, advice, opinion, influence, or command. In English, the word 'authority' can be used to mean power given by the state or by academic knowledge of an area .-Authority in Philosophy:In...

 were distinguished by different terms. Imperium, referred to the sovereignty

Sovereignty

Sovereignty is the quality of having supreme, independent authority over a geographic area, such as a territory. It can be found in a power to rule and make law that rests on a political fact for which no purely legal explanation can be provided...

 of the state

Sovereign state

A sovereign state, or simply, state, is a state with a defined territory on which it exercises internal and external sovereignty, a permanent population, a government, and the capacity to enter into relations with other sovereign states. It is also normally understood to be a state which is neither...

 over the individual

Individual

An individual is a person or any specific object or thing in a collection. Individuality is the state or quality of being an individual; a person separate from other persons and possessing his or her own needs, goals, and desires. Being self expressive...

. It is not to be confused with auctoritas

Auctoritas

Auctoritas is a Latin word and is the origin of English "authority." While historically its use in English was restricted to discussions of the political history of Rome, the beginning of phenomenological philosophy in the twentieth century expanded the use of the word.In ancient Rome, Auctoritas...

or potestas

Potestas

Potestas is a Latin word meaning power or faculty. It is an important concept in Roman Law.-Origin of the concept:The idea of potestas originally referred to the power, through coercion, of a Roman magistrate to promulgate edicts, give action to litigants, etc. This power, in Roman political and...

, different and generally inferior types of power in the Roman republic

Roman Republic

The Roman Republic was the period of the ancient Roman civilization where the government operated as a republic. It began with the overthrow of the Roman monarchy, traditionally dated around 508 BC, and its replacement by a government headed by two consuls, elected annually by the citizens and...

 and empire

Roman Empire

The Roman Empire was the post-Republican period of the ancient Roman civilization, characterised by an autocratic form of government and large territorial holdings in Europe and around the Mediterranean....

. Primarily used to refer to the power that is wielded, in greater or lesser degree, by an individual to whom it is delegated, the term could also be used with a geographical connotation, designating the territorial limits of that imperium.
In ancient Rome, imperium could be used as a term indicating a characteristic of people, the wealth held in items, or the measure of formal power they had.