The term originates from the Latin translation of Greek word politeia. Cicero, among other Latin writers, translated politeia as res publica and it was in turn translated by Renaissance scholars as "republic" (or similar terms in various western European languages).
The term politeia can be translated as form of government, polity, or regime and is therefore not always a word for a specific type of regime as the modern word republic is. One of Plato's major works on political science was titled Politeia and in English it is thus known as The Republic. However, apart from the title, in modern translations of The Republic, alternative translations of politeia are also used.
However, in Book III of his Politics, Aristotle was apparently the first classical writer to state that the term politeia can be used to refer more specifically to one type of politeia: "When the citizens at large govern for the public good, it is called by the name common to all governments (to koinon onoma pasōn tōn politeiōn), government (politeia)". Also amongst classical Latin, the term "republic" can be used in a general way to refer to any regime, or in a specific way to refer to governments which work for the public good.
In medieval Northern Italy, a number of city states had commune or signoria based governments. In the late Middle Ages, writers such as Giovanni Villani began writing about the nature of these states and the differences from other types of regime. They used terms such as libertas populi, a free people, to describe the states. The terminology changed in the 15th century as the renewed interest in the writings of Ancient Rome caused writers to prefer using classical terminology. To describe non-monarchical states writers, most importantly Leonardo Bruni, adopted the Latin phrase res publica.
While Bruni and Machiavelli used the term to describe the states of Northern Italy, which were not monarchies, the term res publica has a set of interrelated meanings in the original Latin. The term can quite literally be translated as "public matter". It was most often used by Roman writers to refer to the state and government, even during the period of the Roman Empire.
In subsequent centuries, the English word "commonwealth" came to be used as a translation of res publica, and its use in English was comparable to how the Romans used the term res publica. Notably, during The Protectorate of Oliver Cromwell the word commonwealth was the most common term to call the new monarchless state, but the word republic was also in common use. Likewise, in Polish the term was translated as rzeczpospolita, although the translation is now only used with respect to Poland.
Presently, the term "republic" commonly means a system of government which derives its power from the people rather than from another basis, such as heredity or divine right.