What is Republic?

Legal Definition
A republic (from Latin: res publica) is a sovereign state, country, or government which is organized with a form of government in which power resides in elected individuals representing the citizen body and government leaders exercise power according to the rule of law. In modern times, the definition of a republic commonly refers to a government which excludes a monarch. Currently, 147 of the world's 206 sovereign states use the word "republic" as part of their official names; not all of these are republics in the sense of having elected governments, nor do all nations with elected governments use the word "republic" in their names.

Both modern and ancient republics vary widely in their ideology and composition. In the classical and medieval period of Europe, many states were fashioned on the Roman Republic, which referred to the governance of the city of Rome, between it having kings and emperors. The Italian medieval and Renaissance political tradition, today referred to as "civic humanism", is sometimes considered to derive directly from Roman republicans such as Sallust and Tacitus. However, Greek-influenced Roman authors, such as Polybius and Cicero, sometimes also used the term as a translation for the Greek politeia which could mean regime generally, but could also be applied to certain specific types of regime that did not exactly correspond to that of the Roman Republic. Republics were not equated with classical democracies such as Athens, but had a democratic aspect.

Republics became more common in the Western world starting in the late 18th century, eventually displacing absolute monarchy as the most common form of government in Europe. In modern republics, the executive is legitimized both by a constitution and by popular suffrage. In his work, "The Spirit of the Laws", Montesquieu classified both democracies, where all the people have a share in rule, and aristocracies, where only some of the people rule, as republican forms of government.

Most often a republic is a single sovereign state, but there are also sub-sovereign state entities that are referred to as republics, or that have governments that are described as 'republican' in nature. For instance, Article IV of the United States Constitution "guarantee[s] to every State in this Union a Republican form of Government". In contrast, the Soviet Union was constitutionally described as a "federal multinational state", composed of 15 republics, two of which – Ukraine and Belarus – had their own seats at the United Nations.
-- Wikipedia
Legal Definition
A commonwealth; that form of government in which the administration of affairs is open to all the citizens. In another sense, it signifies the state, independently of its form of government. 1 Toull. n. 28, and n. 202, note. In this sense, it is used by Ben Johnson. Those that, by their deeds make it known, whose dignity they do sustain; And life, state, glory, all they gain, Count the Republic's, not their own, Vide Body Politic; Nation; State.
-- Bouviers Law Dictionary
Legal Definition
A commonwealth; a form of government which derives all its powers directly or indirectly from the general body of citizens, and in which the executive power is lodged in officers chosen by and representing the people, and holding office for a limited period or at most during good behavior or at the pleasure of the people, and in which the legislative power may be (and in modern republics is) entrusted to a representative assembly. See Federalist, No. 39; Republic of Mexico v. De Arangoiz, 5 Duer (N. Y.) 636; State v. Harris, 2 Balley (S. C.) 599. In a wider sense, the state, the common weal, the whole organized political community, without reference to the form of government; as in the maxim interest reipublicae ut sit finis litium, Co. Litt. 303.
-- Black's Law Dictionary
Legal Definition
Same as Republican government.
-- Ballentine's Law Dictionary