Traveller comes in many editions, and its rules and assumptions vary between them. The following will be most relevant to
Classic Traveller (CT) and
Mongoose Traveller (MGT), both being relatively popular versions. Mega Traveller (MT) and Marc Miller's Traveller/Traveller 4th Edition (T4) are also similar in many aspects but different in others. There are also Traveller: New Era (TNE) using a variant the Twilight:2000 rules, Traveller D20 (T20), GURPS: Traveller and Traveller Hero; these versions differ in many ways from CT, MT, T4 and MGT.
So let's get into Traveller itself. Traveller (originally published in 1977) was originally designed to be a generic sci-fi ruleset compatible with a wide array of sci-fi settings, especially of the 1960's-1970's interstellar kind. All editions of Traveller come with many world-building rules - random world generation, ship-design systems, and in some cases alien critter ("animal") generation systems and vehicle design systems. It is entirely possible to build your own setting for Traveller and ignore any official setting material - in fact, the original rules has no official setting at all!
However, Traveller has long been associated with the Official Traveller Universe (OTU), an Asimov-style (so I've been told) space-opera affair centered on the Third Imperium. The Imperium is a huge quasi-feudal interstellar state encompassing 11,000 worlds (most of which have either official or unofficial stats!); during th Classical Era - covered by both Classic Traveller and Mongoose Traveller - it was mostly a stable society, despite occasional wars with its surrounding states. Several official alien races also exist, such as the felinoid Aslan, the caninoid Vargr, the reptilian (but with an insect-style society, metamorphoses and biological castes) Droyne, the psionic human Zhodani, the Terran-nationalist Solomani, the militant herbivore K'Kree and the weird, manipulative Hivers. The OTU feels like 1960's-1970's sci-fi and is a bit technologically conservative (very little cybernetics, not many AIs around until TNE, little focus on computers). The Imperium is also anti-psionics, unlike other politics (such s the Zhodani, who are ruled by psions).
The basic Traveller game mechanic is roll 2d6+skill level+modifiers; a roll of 8 or more is a success. Skills usually range between 0 and 3 but could be higher; characteristics (ability scores) usually range from 2-12, with 1 or 13-15 in extreme cases. Classic Traveller has several varieties of this mechanics for different uses, but MegaTraveller and Mongoose Traveller use a coherent "task system" with coherent characteristic (ability) modifiers. Difficulty is also a die modifier in most versions.
Traveller is skill-based. At their heart, characters have six characteristics (Strength, Endurance, Dexterity, Intelligence, Education and Social Standing) and a number of skills. In Classic Traveller, your entire "character sheet" (other than gear, money and ships, of course) could be summarized in a single short paragraph! There is a wide range of skills, from Admin (a social skill used to deal with bureaucracies) through things such as Gun Combat (several skills, depending on which kind of guns you want to use) and Pilot (used for piloting starships) to Medic and Vehicle skills. At its core, Classic Traveller had 27 skills; later versions have more diverse skills.
Character creation is semi-random and based on resolving the character's pre-adventuring career. Traveller characters start the game as experienced adults rather than 18-years-old beginners. Most character development (in the game-mechanics sense) takes place during character generation; during play, most character development is in terms of knowledge, personality, possessions and political power, while acquiring new skills is a very slow process. But that's OK, since you could start the game as a very experienced professional!
Traveller technology mostly has a "hard science" feel to it. Sure, there are anti-gravity vehicles, reactionless drives, psionics and jump (read: FTL) drives, but other for these the technology seems very plausible and even "conservative" (AIs are rare and there is almost no nano-tech to speak of). The majority of ground weapons are slug-throwing guns, with energy weapons typically being heavy support weapons.
Combat is fast, rules-light (yet, in Mongoose Traveller, covering a surprisingly wide range of possibilities for its mere 9 pages) and deadly. Very deadly. While a typical character has a good chance of surviving a gun shot, each shot is very damaging and two or three shots (or even one in some occasions) would kill each character. Combat uses the same basic "2d6+skill+modifiers for 8 or more" mechanic as any other skill roll; things such as range or cover modify that roll. Damage is subtracted directly from the target's physical characteristics; when two are reduced to zero, the character becomes seriously wounded and unconscious; when all three are zeroed the character is killed. Vehicle and ship combat uses hit-location tables (listing things such as weapons, drives, passengers, fuel etc).
