It obviously isn’t possible to completely explain the extensive background material created for the Traveller universe over almost five decades of publication by multiple companies, but a quick summary may be helpful.
No faster-than-light communication exists, so messages must be carried by starships. As each jump takes roughly a week regardless of distance, and has a limited range depending on the ship’s drive and fuel capacity, this limits speed of response. This in turn requires governments to give worlds and sectors considerable local authority to deal with emerging threats or problems in a realistic timescale; even at maximum jump, a message from the imperial frontier would take around a year to reach Capital and a reply to come back.
The primary human state is the Third Imperium. This provides for mutual defence and enforces some basic minimums, such as banning slavery, but otherwise allows member worlds considerable autonomy. Individual Imperial worlds can thus differ significantly in government type, culture and even level of technology available. The Imperium has a “working” nobility as part of its system of government, though the power of nobles and how directly they are involved in government also varies considerably.
The Solomani Confederation is an offshoot of the Imperium, but the two have a historically antagonistic relationship. Solomani culture is broadly similar to that of the Imperium (insofar as there can be said to be a common “Imperial culture”) but it is a one-party state, with only the Solomani Party allowed. However, branches of the party on different worlds can differ significantly in both doctrine and its implementation. Imperial propaganda generally portrays the Confederation as a police state, with Solomani State Security (“SolSec”) constantly monitoring every citizen. There is some truth in this, and SolSec monitors are omnipresent, but on many worlds a majority of citizens truly believe in the Solomani Cause.
Psi powers are known to exist in a small percentage of humans, but their training and use have been outlawed in both the Imperium and the Solomani Confederation since the Psionic Suppressions of the 800s, after issues of gross misuse by psions, and are very rarely encountered in these areas.
The Zhodani are the third major human state. They are biologically human, descended from people transplanted from Earth 300,000 years ago by the mysterious “Ancients”, who later destroyed themselves in a cataclysmic war. However, the Zhodani developed psionics early in their history, and their culture has incorporated routine use of such powers for thousands of years. With the ability to know whether someone is telling the truth or not, and being able to determine exactly what psychological techniques work and how well, crime and mental illness are almost completely absent in Zhodani society.
The Zhodani Consulate is ruled by a psionic nobility; children from prole families who score highly on standardised psionic tests in their early years at school are adopted into the intendent class, and will ultimately work their way into the nobility through service. The Tavrchedl’ regularly monitor the opinions and mental health of all Zhodani citizens; Imperials translate their title as “Thought police” and assume their role is to quash dissent, whereas the Zhodani maintain they are the equivalent of paramedics or firefighters, dealing with citizen’s problems to enable them to live happy, healthy and fulfilled lives
The Zhodani and the Imperium have fought a number of frontier wars, including a relatively recent one (the Fifth Frontier War, 1107-1110), due to mutual fear; the Imperials believe Zhodani citizens are literally brainwashed into happiness and compliance, while the Zhodani regard the Imperium as a barbaric anarchy where lying, deceit, insanity and criminality go unchecked.
There are five primary non-human races in the setting; as a generalisation, Aslan and Vargr technological level is slightly lower than that of humans, while the Hivers are equal in most areas and superior in computing. There are also dozens of minor human and non-human cultures, with technology varying from human maximum to stone tools.
The Vargr are a bipedal species created from early canid (ie wolf) stock by the Ancients around 300,000 years ago, and spread to a number of sites across the universe in the same way as protohumans. Physically, Vargr are a little smaller and slighter than humans, but within human norms.
Intellectually, Vargr have similar drives to humans, though they are much more strongly influenced by a leader's "charisma" and persuasiveness than humans – Vargr are rarely interested in what the rules or some bureaucracy say should be done, but they will respond quickly and well to identical instructions from a Vargr they respect or admire.
Humans often see Vargr societies as chaotic, and while there is some justice in this, it is not the whole truth. Vargr can be very loyal to a leader and maintain that loyalty through hard times, so long as they continue to believe in the leader. However, if they lose confidence in the leader or a more charismatic one comes along, they will regard it as perfectly normal to transfer their loyalty.
Vargr are much more comfortable with direct loyalty to a leader, and thus it is hard for them to build large scale societies – if subordinate leaders lack charisma then Vargr will not follow them, but on the other hand, subordinate leaders with lots of charisma are easily able to strike out on their own with their immediate followers rather than remain subordinate. There is thus no single Vargr state, and the "Vargr Extents" contain a bewildering array of governments and organisations whose power and territory can endure for many years, or shift abruptly.
Similarly, Vargr are unlikely to be especially loyal to abstract concepts – a Vargr would find nothing odd in a career that started out as a police officer, turned pirate when the opportunity presented itself, and moved back to law enforcement if the leader who had inspired them to turn pirate was killed – neither occupation makes them "good" or "bad" Vargr; they were just doing what seemed best at the time.
Vargr, of course, would say that this is exactly what humans do when they are conscripted into the military; serving a term as (say) a soldier doesn't mean that human is especially likely to kill other humans in future, as they were just doing what was needed during the war and changed back when their circumstances changed.
Vargr are often stereotyped as "Corsairs" by human media, and while some of this is xenophobia and propaganda, just as much is simply because those Vargr who do become corsairs are much more visible to human news-crews. Billions of Vargr within the extents live perfectly normal lives as factory workers, accountants and shopkeepers, but their activities are rarely newsworthy or visible to humans within the Imperium.
Historically, the Vargr have generally been Zhodani allies, though this is merely an alliance of convenience against the Imperium. The borders between the Vargr and the Imperium are turbulent, since any state the Imperium signed a pact with might or might not be long-lasting, but would have only limited control over the Vargr living within it even while it did last – any charismatic leader who could talk a group of Vargr into following them and can buy or steal a ship can lead a corsair expedition at any time, without feeling bound by "state policy".
The Aslan are also bipeds, descended from carnivore chaser / pouncer stock. They are a little larger than humans at an average of 100 kg each, and have a folding "dewclaw" in each hand, originally used to dispatch prey and still used for that purpose, as well as in duels between Aslan.
Aslan society is highly gendered. Males are concerned with politics and war, and fill occupations such as pilot, gunner or soldier. However, they are not expected to really understand concepts such as money. Females are concerned with commerce, research and engineering and might run corporations, conduct scientific research or serve as starship engineers. Aslan will normally assume that humans filling a role are the "correct" gender for that role and treat them accordingly, even if it doesn't match the human's biological sex.
Aslan society is also very concerned with honourable conduct. This differs for males and females, but is defined by well-established custom – dishonourable actions include cowardice, breaking ones’ word or theft by stealth. Taking something by force may or may not be dishonourable, depending on circumstance, and things concerning money generally do not affect male honour, as they are not expected to understand it. An Aslan who has lost his or her honour is nothing, and is likely to either go into exile or even commit suicide, rather than live disgraced. Aslan who feel their honour has been insulted will generally challenge the person responsible to a duel.
Aslan society is based on extended families, and clans above that. Clans may have other clans as vassals or allies, and an alliance of the 29 most powerful clans (the Tlaukhu) forms the effective government of the Aslan Hierate.
Aslan males attach great value to owning land. While land obtained by purchase is perfectly acceptable, it is rare for an Aslan clan to sell land except in the most desperate circumstances. Thus while the eldest sons of a clan will inherit the family land, population pressure pushes any Ihatei (literally, "Second sons") either into trying to conquer their neighbours, or towards the frontier where they can find new land either by exploration or by conquering non-Aslan worlds.
Aslan borders with the Imperium are secured by treaty, but those with the Solomani are not, and the same goes for the number of small buffer states between Imperial and Aslan territory.
The Hivers are the most physically and mentally alien of the major races. Physically, Hivers are six-limbed starfish-like scavengers weighing around 150kg each. They have no auditory sense or vocal apparatus, and communicate between themselves using a gestural language, though any Hiver dealing with humans will have a translator / voice synthesiser able to turn keypad input into spoken anglic. Given Hiver skill with computers, these synthetic voices can be very life-like, and even mimic human emotion.
Hivers are hermaphrodites with no interest in sex or rearing children; larva are not intelligent and Hivers have no protective feelings toward them until they are several years old and have developed enough intelligence to be worth educating.
Equally, while Hivers use money as a medium of exchange, and some Hiver merchants seem to regard it as a way of "keeping score" of how successfully they are trading, personal wealth or poverty don't seem to have any particular social connotations for Hivers, and they will not generally do something purely to earn cash beyond their immediate needs unless they will require it for some future project.
Without any of these key drivers for humans, Hivers are motivated instead by intellectual curiosity and interest in a particular field or hobby, which might be anything from stamp collecting or Aslan history to military strategy. Hivers typically form clubs of various types to pursue these hobbies, where humans might form companies or even states, and some of these are relatively powerful – the Hiver homeworld is effectively run by a club interested in planetary administration, for example.
Hivers particularly enjoy getting other sentients or (ideally) other Hivers to carry out their plans by manipulating them – one of the most respected social accolades a Hiver can receive from his peers is the award of the coveted formal title "Manipulator".
Hivers are generally physical cowards (or "sensibly cautious" as they would term it) though they have no ethical issue with bloodshed provided it isn't happening to them, and one of their client races (the epically-violent and raucous Ithklur) have found a niche as the Hive Federation's ground troops and marines. The Hive Federation is not territorially aggressive and its borders with the Imperium are peaceful, though conspiracy theorists insist that is simply because the Hivers would much rather take over the Imperium from within.
The Droyne are a psuedo-reptilian race divided into six anatomically distinct castes that are adapted for particular roles in Droyne society. For example, leaders are more intelligent and better educated, warriors and workers are stronger and hardier, while sports are more self-reliant and are the only Droyne who can exist for prolonged periods away from a Droyne community.
Physically, Droyne are a relatively slight race, with hollow, birdlike bones to reduce weight at the cost of making them less robust. Most are only a metres or so tall, while even the bigger castes are smaller than an adult human. All have six limbs plus a tail – two arms, two legs and a pair of wings which would allow them to fly on a low gravity world with a dense atmosphere, which is presumably what their unknown homeworld was like.
Almost all Droyne have a notably communal mindset, always prioritising what is important to the community over their own needs, and it is often hard to identify Droyne personalities except for leaders and sports – almost all Droyne workers seem very similar, for example. Their motivations are often so different that they are hard for humans to understand, though they will always be based around the good of their group.
Droyne communities are widely scattered across charted space, and it is theorised that they were dispersed by the Ancients in the same way as humanity. While some are primitive, others have technology up to early stellar standards. There is evidence that at least some Droyne may possess psionic powers, but the difficulty of conducting research means that little is known for certain.
Droyne seem to be related to a species known as Chirpers, who are similar but not identical to Droyne physically, but apparently only semi-intelligent.
Though the player characters will not know it, the Ancients were actually a superior form of the Droyne (effectively a single super-genius individual and his descendents) who destroyed themselves in a cataclysmic civil war. Chirpers are actually Droyne who have not gone through the casting phase of their life and are thus effectively trapped in an immature form rather than having developed into one of the normal castes.
Finally, the K'kree are six-legged herbivore grazers who will not tolerate any meat-eating species in the universe. Fortunately, they are handicapped by being steppe creatures with powerful social bonds and a claustrophobic reluctance to enter confined spaces. Space travel is thus rare and difficult for them, and they do not currently have a border with any of the major human polities. No edition of Traveller has done much with the K'kree that I'm aware of, and they will almost never be encountered outside their own space