Although it has also been borrowed by other works, such as Terry Pratchett's Discworld novels, the term "gnoll" is not one that's native to folklore or legend. Gygax borrowed the word from a short fantasy story by Lord Dunsany, in which it is used to describe sinister woodland beings. Although Dunsany never described what his "gnoles" looked like, Gygax has stated that he took the word to mean that they were supposed to resemble a cross between a gnome and a troll, which is as plausible an etymology as any.
By the time of the 1E Monster Manual, however, he had already switched to the "hyena man" look that they have kept ever since. This appears to be original to D&D.
Beginning with the first Monster Manual, then, gnolls are said to have a "great resemblance" to hyenas... but neither the illustration, nor the rest of the descriptive text bear this out. Instead, we have a tall humanoid being, hairy and with clawed feet, with a low forehead, large teeth, and a long, vaguely pointed, snout. Oddly, they seem to have one toe that points backwards from their heel. Their skin is said to be greenish-grey, implying that their hair doesn't form a thick pelt, save for a mane on the back of the head, which is reddish to yellow in colour.
Gnolls form the highest rung on a straightforward game mechanical hierarchy of the five "evil tribal humanoid" races (the hierarchy continues on up, but, above gnolls, the races cease to be tribal). Compared with orcs, they have a 10% higher chance of landing a blow, a 5% lower chance of being hit in return, and do just marginally more damage when they attack. They are the only race of the five to have two hit dice, giving them double the hit points of orcs, and, on average 1½ more than hobgoblins, which occupy the rung in between.
If orcs are balanced against first level characters, therefore, gnolls are balanced against second level, although, given that they are often found in large numbers, they'd be more suitable opponents for a level or so above that. Essentially, they're something to move on to once orcs cease to be enough of a challenge.
A key difference, however, is that gnolls are the only such race to be described as "chaotic" evil, rather than lawful, and they're also even less intelligent than the other four. However, this doesn't really seem to play out much in the rest of the description, beyond the fact that are normally only fluent in two or three distinct languages, rather than four.
Gnoll communities average just under 400 members, which is slightly smaller than that of their weaker counterparts. However, well over half of these are children, implying mortality rates even higher than among hobgoblins. Males outnumber females by two to one, as they do amongst orcs, and, as usual, its implied that the latter are non-combatant and low status.
Given how chaotic they are supposed to be, they are remarkably co-operative with other races, and with other tribes of their own kind. They are particularly associated with trolls, and are often accompanied by hyena packs. Given that they live in all but the harshest of environments, and hyenas are resolutely tropical, this must mean either that they carry them with them from elsewhere, or that the animals are more widespread in their world than ours.
(As an aside, they are also mentioned as associating with hyenadons. In 1E D&D however, this term is used to refer to giant hyenas, and not to the real world animal of the same name, which is something else entirely).
The descriptive text for gnolls remains the same in this edition, beyond the fact that they are now marginally taller, at 7½ feet (230 cm). The illustration, however, shows a being with a thick pelt of fur all over, patterned like that of a spotted hyena (the largest of the three real-world species alive today), and without the mane mentioned in the text. A hump above and behind the shoulders pushes the head forward, reminiscent of the high shoulders of quadrupedal hyenas, but the head is shaped more like that of a jackal.
Gnolls, already one point lower than orcs and goblins, lose a further point of intelligence in this edition, but, once again, seem to be remarkably well organised. They have lost the automatic ability to speak the language of trolls, although they still commonly cooperate with them, perhaps because of Gygax's original concept that the two races were related. The young now outnumber the adults by a staggering two to one. Females, however, can now fight as effectively as their menfolk, but have a lower status in society, perhaps because of the time they have to spend raising all of those children.
As before, gnolls keep a number of humanoid slaves, which they use as often for food as for labour. They are implied to be purely carnivorous, denuding the land around them of wildlife, and deeply sadistic, preferring to eat only after causing as much pain as possible. They are stated to be nocturnal.
Their demographics have changed, too. Communities are now much smaller, averaging a little over 200 members, as befits a race that's supposedly chaotic (and, in fairness, they're pretty obviously not lawful). The proportion of those that are young is also down, now merely equalling the number of adults - which is still huge by human standards. Perhaps they give birth to litters (hyenas commonly have twins), because, if not, the females must spend a lot of their time pregnant.
It's even clearer now that hunger and aggression are their driving appetites, but while they still eat humans, sadism is no longer specifically mentioned. They do, however, have a small number of spell-casters, mostly priests that follow the god of slaughter.
The illustration shows a creature that has the same physical build and appearance as the 3E sort, but with far less fur, clearly showing the greyish skin of the 1E version. They retain the reddish mane, and the fur they do have has the pattern of a spotted hyena, as before. With the old stepwise progression of the races having gone, they're now reasonably balanced with orcs, being less strong, fit, and intelligent, and with lower combat skills and damage potential, but having better armour and noticeably more hit points.
There has, however, been an even more dramatic change in what gnolls actually are. They're no longer regular humanoids, like orcs or goblins, but sexless beings with an ultimately demonic origin. This is because young gnolls, formerly so common, no longer exist at all, with new gnolls being magically created from regular hyenas. It's implied that they have no other way of reproducing, which, once again, implies that hyenas must be much more common and widespread than on our world.
The description of what passes for their culture is now indisputably chaotic. They rampage across the landscape like locusts, a violent and hungry horde with little in the way of organisation, and no magic beyond the ability to create others of their kind. Where, previously, they often cooperated with orcs, trolls, and other evil races, they are now quite incapable of doing so and will turn on each other if no external enemy presents itself. Uniquely among the five original tribal races, they still eat human flesh.
As gnolls have evolved over the various editions, then, they have become steadily more bestial, both in appearance and personality. In a reflection of this, their intelligence, always the lowest of the five races, has steadily dropped further. Where previously, there was little justification for their "chaotic" descriptor, they're now pretty much the epitome of what a chaotic evil culture would look like, disorganised packs fuelled only by their indiscriminate hunger.
Since many of them were created before the re-interpretation of the race, most published D&D settings describe gnolls as similar to other humanoids. Even Forgotten Realms has made it clear that gnolls reproduce in the normal manner, with one book set in that universe even indicating that they can cross-breed with humans (but rarely do so). On the other hand, despite ostensibly being set in the same universe, since it's written for 5E, Volo's Guide uses the newer, seemingly incompatible, version.
In Mystara and, to a lesser extent, Eberron, they have crudely organised nations, and, in the latter, they are said to be a "force for stability" amongst warring monster factions.
In Pathfinder/Golaron, gnolls mostly live in deserts, like the rarer striped hyenas of our world, although some inhabit savannah country, as their more obvious counterparts, the spotted hyenas, do. They are specifically stated to give birth to litters, and they feed mostly on carrion, rather than the fresh meat favoured by their kind in other game worlds. Oddly, they have a "chaotic" society with strictly enforced rules of cooperation that emphasise the needs of the group over those of the individual.
In other systems, designing gnolls requires them to have higher strength, and especially physical resilience, than other humanoids, although not at superhuman levels. They have a particularly low intelligence for sentient beings, and will have disadvantages relating to an insatiable rage or bloodlust, as well as (in most conceptions) the unsavoury habit of eating other humanoids. Beyond that, they seem to have few useful skills outside of combat, save anything they might use to scavenge for food.