Numerous definitions can be applied to the term commonwealth. In its loosest form, the term means for the common or public good, and is often a state formed for the common good of the people. It can also apply to a group of nations that have a loose alliance for the good of all members of each nation.
Several US states have commonwealth designation. These are Virginia, Massachusetts, Kentucky, and Pennsylvania. The designation was important as these states originally defined their governance in direct opposition to the governance of the British Empire. The designation now lacks meaning and has merely been retained as a salute to the past history of rebellion that freed the US from British rule.
Some US territories are also organized as commonwealths. These territories, like Puerto Rico, are not entitled to the same rights and benefits as recognized states. For example, Puerto Rico’s designation as a commonwealth implies an ongoing relationship with the US, but does not imply statehood.
One of the largest is the Commonwealth of Nations, nations formerly part of the British Empire. This group is headed by Queen Elizabeth II and implies fellowship, but not rule, over former British territories like New Zealand and Canada. The Commonwealth of Nations includes 53 nations, each with their own self-governance.
Another large commonwealth is the alliance of over 10 countries formerly belonging to the USSR. These ties can often help smaller countries gain larger political power because of the unifying force of the group. The commonwealth of this type, however, does not hold the same type of political power as, for example, the United Nations. But those countries belonging to the United Nations may gain strength by voting together for those issues which are likely to impact them most.
A commonwealth does not necessarily imply the same sort of government. Alliances connecting nations may be composed of monarchies, democracies and socialist states. Most often, the association is thought of as somewhat democratic or republic in principal, with a greater value on individual rights of people, and public influence in the political process.