The Azadians are the major species described in The Player of Games. The Azadians are a humanoid race with various peculiar physical and societal parameters; their society is called the Empire of Azad.
Generally humanoid, with short legs, their faces are described as slightly bloated, flat and pale. (These would be relative to a Culture norm, not an Earth one.) Most crucially however, Azadians are composed of three sexes - a 'male' having a penis whose sperm is then fertilised by an 'apex' sex which has ovaries and a 'reversible vagina' used as an ovipositor to implant the fertilised eggs in the 'female' sex.
Stemming from the Planet Eä in the Lesser Magellanic Cloud, the Empire of Azad is, by the time it is contacted by the Culture, a major stellar empire, ruled by a single emperor and an imperial bureaucracy - something described as very rare in the universe of the Culture, as such systems are considered too inflexible to produce the technological advances required for a stellar society. Their success is at least partially attributed to the eponymous game of Azad, which plays a central role in their society and has existed since before the Azadians started colonising other worlds.
The technological level of the empire is described as being much lower than the Culture's, though it seems to be in contact with enemies of the Culture who sometimes furnish it with Culture-equivalent technology.
At the end of The Player of Games, the Empire of Azad is in massive internal turmoil based on the results of Culture intervention. It is implied that this was the result sought by Special Circumstances, who see the upheaval as an opening for change to a more advanced, more Culture-like society.
In Banks' story, the distinction of three sexes causes even harsher social stratification between the genders than found in humanity, with the 'apex' sex being the clearly - and harshly - dominant sex. In addition to this factor, two other elements shape their society.
The game of Azad - often just 'The Game' - is not only a testing mechanism for entry (at all levels) into the various branches of bureaucracy, military and other careers of the Empire - up to the very post of the Emperor belonging to the best player of the game. It also serves to influence or directly determine the current governing strategies, political faction fights and multiple other elements of Azad's society. It is, in short, a philosophy and a governing system, all played on multiple extremely complex room-sized boards shaped like layered pyramidal landscapes, and using various holographic pieces as well as playing cards and other elements. While the game is not the only way of resolving conflicts in the Empire (assassinations, for example, are also a possibility), even conflicts on the board can take on a deadly edge, with participants sometimes wagering submission to violence (sexual and otherwise), the amputation of body parts, or their lives outright.
This leads to the final element strongly influencing their society, namely the fact that Azadian society has an extremely strong undercurrent of physical and emotional cruelty. While only the lower classes celebrate this sadism in the open, the perversions of the upper classes are all the more imaginative, with whole television networks available only to the elite being devoted to snuff and torture.
As a result, Azadian society is highly stratified, and while outwardly pompous and grand, also marked by deep moral corruption, which galvanises the Culture's representatives into direct action.