What is Commonwealth?

Legal Definition
Commonwealth is a traditional English term for a political community founded for the common good. Historically it has sometimes been synonymous with "republic".

The noun "commonwealth", meaning "public welfare; general good or advantage" dates from the 15th century. Originally a phrase (the common-wealth or the common weal – echoed in the modern synonym "public weal") it comes from the old meaning of "wealth", which is "well-being", and is itself a loose translation of the Latin res publica (republic). The term literally meant "common well-being". In the 17th century the definition of "commonwealth" expanded from its original sense of "public welfare" or "commonweal" to mean "a state in which the supreme power is vested in the people; a republic or democratic state". "Better things were done, and better managed ... under a Commonwealth than under a King." Pepys, Diary (1667)

The term evolved to become a title to a number of political entities. Three countries – Australia, the Bahamas, and Dominica – have the official title "Commonwealth", as do four U.S. states and two U.S. territories. More recently, the term has been used to name some fraternal associations of nations, most notably the Commonwealth of Nations, an organization primarily of former territories of the British Empire, which is often referred to as simply "the Commonwealth".
-- Wikipedia
Legal Definition
Government. A commonwealth is properly a free state, or republic, having a popular or representative government. The term has been, applied to the government of Great Britain. It is not applicable to absolute governments. The states composing the United States are, properly, so many commonwealths.

2. It is a settled principle, that no sovereign power is amenable to answer suits, either in its own courts or in those of a foreign country, unless by its own consent. 4 Yeates, 494.
-- Bouviers Law Dictionary
Legal Definition
The public or common weal or welfare. This cannot be regarded as a technical term of public law, though often used in political science. It generally designates, when so employed, a republican frame of government,β€”one in which the welfare and rights of the entire mass of people are the main consideration, rather than the privileges of a class or the will of a monarch ; or it may designate the body of citizens living under such a government.

Sometimes it may denote the corporate entity or the government, of a jural society (or state) possessing powers of self government in respect of its immediate concerns, but forming an integral part of a larger government, (or nation.) In this latter sense, it Is the official title of several of the United States, (as Pennsylvania and Massachusetts,) and would be appropriate to them all. In the former sense, the word was used to designate the English government during the protectorate of Cromwell. See Government; Nation; State. (State v. Lambert, 44 W. Va. 308, 28 S. E. 930.)
-- Black's Law Dictionary
Legal Definition
The public; the state; the body politic; England during the Interregnum, 16491660.
-- Ballentine's Law Dictionary