Res publica, also spelled rēs pūblica to indicate vowel length, is a Latin phrase, loosely meaning "public affair".
The most essential characteristic of a res publica was liberty (libertas), which meant freedom from the arbitrary control of another and the absence of a monarchical domination over the body politic, that was analogous to the absolute power of a master over a slave.
From these examples, it also follows that probably there was also a gradual shift of meaning of the res publica concept throughout the Roman era: the "(Roman) Republic" connotation of res publica is something that rather occurs with retrospect to a closed period (so less apparent in Cicero's time, who never knew the era of the Emperors, and could only compare with the epoch of the Kings); on the other hand the translation of the Greek "politeia" concept appears to have nearly completely worn off in late antiquity.
When Pliny dedicates his Naturalis Historiae to his friend Emperor Vespasian in the first century, he uses the word res publica (Latin from LacusCurtius website / 1601 Philemon Holland translation from http://penelope.uchicago.edu/holland/index.html / 1855 John Bostock translation from the Perseus website): When under an Emperor, that is Vespasian or his predecessors, Pliny was not talking about the Roman Republic, but used "commonwealth"/"republic" in the meaning of "the state".
The ambiguity of Rome still considering itself formally, or just "pro forma", a republic throughout the era of the principate, when a monarchic rule had already de facto been established, adds to the complexity of translating "res publica" in this context.
Here the word is used to convey the generic meaning of "public affair" or "the commonwealth" (in contrast to the private or family life) without the Roman connotations of republicanism.
Compare also to the 2nd quote from Tacitus above: there an expression different from res publica and imperium Romanum is used for referring to "the (Roman) State" in general.
Meaning "the Roman Republic" as era with a distinct form of state organisation, from the same book: Later calques of Res publica: