Commonwealth can be described as a gathering of countries or states that share the same ruling and governing structure. It is a term that is widely used in the United States to describe different states. Instead of being called states they are called commonwealths. The term is most associated with the British Commonwealth of nations.
These are the four mainland British countries of England, Scotland, Wales, and Northern Ireland along with all of the countries and possessions that the British monarchy and crown has rule over. While a lot of these territories have their own native and soverign rules and laws, they still pay adherence to the British throne with Canada being a prime example of that. The word commonwealth simply describes the fact that these countries and territories share a common origin and ruler in which the case is Queen Elizabeth II and the British throne.
All of these countries under the British Commonwealth have always been known for showing great pride in being a part of the monarchy of nations which is another interesting trait in a commonwealth country, nation, or state.