The Commonwealth of Nations (generally referred to as simply "the Commonwealth", because nobody's likely to think you're talking about some ''other'' commonwealth these days) is simply put, (mostly) former members of The British Empire who still maintain some sort of symbolic connection with the UK, and, just as importantly, each other.
In its modern form it is more of a beneficial trade, defence and immigration pact than an empire, but about one-third of the nations also have the British monarch as their head of state (these nations are the Commonwealth realms), giving her the same theoretical veto powers outlined in British Political System, while the Judicial Committee of the Privy Council in London is a final court of appeal for some member states. Confusingly, not all Commonwealth Realms have appeal to the Judicial Committee (e.g. Canada and Australianote ), while not every country that retains appeal to the Judicial Committee is a Commonwealth Realm (e.g. Mauritius, which is a Commonwealth Republic, and Brunei, which is a monarchy within the Commonwealth that has its own Sultan). After all, if the institutions made perfect sense, they wouldn't really be British, would they?
Member states sometimes enjoy beneficial trade agreements and the ability to emigrate to other member states more easily than a non member. Commonwealth nations tend to share such characteristics as drinking tea, playing cricket, driving on the left-hand side of the road and using British English spellings—but not all of them (witness coffee-drinking, right-side-driving, and even occasionally baseball-playing Canada, often otherwise regarded as the quintessential Commonwealth Realm). Most of them also use The Common Law as the basis of their legal system.
Mozambique was actually never part of the British Empire, being a former Portuguese territory, but all its neighbour countries were in the Commonwealth and wished to support their poor neighbour, so an exception to the general policy was made. Recently the same thing happened to Rwanda, which has started to adopt more Anglophone trappings and apparently even cricket picked up from Kenya and Uganda.
The terms "Old Commonwealth" (the UK, Canada, Australia, New Zealand, and South Africa) and "New Commonwealth" (everywhere else) are sometimes used, although the terms appear to be declining in usage. Such terms were always controversial given that when coined they were so clearly divided along racial lines (the UK, Canada, Australia and New Zealand being majority-white and South Africa at the time having a white-only government ruling over a disenfranchised black majority, while most of the "New Commonwealth" were black- or Asian-majority former colonies).
They have their own version of the Olympic Games, called the Commonwealth Games, held every World Cup year. Apart from the usual Olympic sports, there are also some more "British" sports such as lawn bowls and netball (cricket has only been played once, at the 1998 games), and Paralympic events are integrated into the Games rather than being a separate event. Their version of the Olympic Torch (and its accompanying relay) is the Queen's Baton, which contains a message from the Queen, whose contents are only disclosed during the opening ceremony. The latest edition was held on the Gold Coast, Queensland, Australia in 2018; Glasgow, Scotland hosted the 2014 Games, while Birmingham, England will host the 2022 Games.
It must be noted that one criterion for joining the Commonwealth is the acceptance of the current British monarch (the Queen) as Head of the Commonwealth (an entirely symbolic title). Although it seems unlikely, non-member countries wishing to join the Commonwealth have not really ever fussed about this provision; rather, it tends to be used as an excuse for states to leave (e.g. the Gambia's 2013 departure on the grounds that the Commonwealth is "imperialistic" at least in part of the whole Queen business, widely considered a ploy to distract the people from local problems.).
The list of member states are:
- Antigua and Barbuda
- The Bahamas
- New Zealand
- Papua New Guinea
- Saint Kitts and Nevis
- Saint Lucia
- Saint Vincent and the Grenadines
- Solomon Islands
- United Kingdom
- Fiji (currently suspended)
- The Gambia (withdrew in 2013 in a surprise move by the increasingly autocratic Yahya Jammeh, who accuses the Commonwealth of being a tool of Western imperialism. Rejoined five years later through his successor Adama Barrow after Jammeh was deposed)
- India (The first ever country that officially severed itself completely from British rule to be admitted)
- Mozambique (actually a former Portuguese colony)
- Rwanda (The second nation to be admitted without any national ties to the UK)
- Sierra Leone
- South Africa (not a member from 1961 to 1994, because of apartheid)
- Sri Lanka
- Trinidad and Tobago
- Ireland (left upon becoming a republic in 1949. Ironically, the fix that allowed India to remain in the Commonwealth as a republic was developed a few months later, but it was too late by then)
- Zimbabwe (suspended indefinitely 2002, withdrew 2003)
A few former British colonies in the Middle East have expressed at least mild interest in joining. Palestine has indicated that it will apply once/if it gets its independence; Israel has indicated it might join at the same time (any attempt to join right now by either of them would be such an invitation for needless rancor that they haven't bothered). Sudan's application was held up by its civil wars; with those now settled, both Sudan and South Sudan have applied, although the former's dictatorial regime prevent it from meeting the criteria (generally speaking, new members are expected to be at least vaguely democratic), and now the latter's instability/civil strife have put those plans on back burner. Yemen has also applied, although its current instability (by which we mean an all-out civil war) has put plans on hold for the moment. Afghanistan, where cricket is rising and which has strengthening ties with India, has expressed an interest in having an interest.
Highlighting the fact that membership is possible for nations that are not former British colonies, in 1956 British Prime Minster Anthony Eden extended an informal invitation for France to join the Commonwealth (with the potential for a complete merger of France and the UK), which French PM Guy Mollet briefly but seriously considered. Though the Normandy region of France was once under English rule. Nor was this even the first time the UK and France considered merging into a single nation.
There is one major country that satisfies all the criteria for Commonwealth membership, but hasnt expressed any interest in joining - The United States. It is eligible due to its initially constituent Thirteen Colonies being British possessions, but having fought The American Revolution to break away. The US lack of interest in joining the Commonwealth is largely due to acknowledgement of Queen Elizabeth II as the Head of the Commonwealth and therefore the one with final authority on all decisions taken by the body, being a compulsory condition for membership. Strong anti-royal political sentiment in the US precludes this.