The term "goblin" is, of course, an ancient one in English, referring to a (usually) malevolent magical being that is typically small and misshapen; a sort of evil fairy. As with orcs, the more modern conception of goblins comes from J.R.R. Tolkien. Indeed, Tolkien uses the word as simply another word for "orc", mainly as the term that hobbits use for that race. The fact that the word therefore ends up being used more frequently in The Hobbit, in which these particular antagonists seem less of a serious threat than their counterparts in Lord of the Rings do, likely combines with the original folklore meaning of the word to produce the "like orcs, only weaker" idea first used in D&D.
Physically, goblins appear rather more humanoid than orcs, but are only around four feet tall. They have broad, flat noses and large teeth, and both their skin and eyes vary from yellow to red. They seem to wear only regular leather armour, but their armour class is the same as that of orcs, presumably because they're harder to hit, being smaller, and possibly more nimble. Their preferred weapons are spears and shortswords, although some (as in the illustration) carry spiked clubs, and a few are apparently specialist slingers, only striking from a distance.
Like orcs, they are demoralised in full sunlight, and they are even more likely to live underground. Also like orcs, they are marginally less intelligent than humans, but are nonetheless always fluent in five different languages. Because of their subterranean habitations, we are told that they have a particular hatred for dwarves and gnomes, rather than for elves, as the orcs do.
They are described as "lawful evil", living in communities with an average population of a little over 500, plus an unspecified number of slaves (likely captured human peasants or the like). They are fond of torture, although, unlike orcs, at least they have no interest in mating with other races. As with orcs, about one in six are tougher than usual, being the leaders and wearing superior armour. Males outnumber females by five to three, with the latter being incapable of fighting, and presumably holding a subservient position in society, although this isn't specified.
They have also domesticated wolves, which, in a nod to Tolkien, they use as riding animals. They also cooperate with bugbears, to which they are said to be related, but not with hobgoblins. Oddly, there is no indication at this early stage, beyond the similarity of names, that goblins and hobgoblins are even related, although a relationship to kobolds is hinted at - surprisingly so, given that the latter are obviously reptiles. (Most likely, this is because, in the real world, the words "goblin" and "kobold" are thought to be etymologically related).
2EAs is usual, 2nd edition AD&D expands on the description of goblins, rather than drastically changing their nature. The only real difference in their statistics is that their intelligence is said to be lower than before, making them stupider than orcs, as well as weaker. They do, however, retain their fluency in multiple languages. In terms of their physical appearance, they are now much scrawnier, and have larger ears, and possibly a somewhat upturned nose. Their eyes are said to be simultaneously "dull" and "gleaming", whatever that may mean, but the colour scheme remains the same.
Since the first edition, the relationship to hobgoblins has been made explicit, although there's still no indication that the two races really cooperate. Indeed, goblins are now said to be cowardly, which probably means that they would run from hobgoblins if they encountered them in equal numbers.
Their society is described as very hierarchical, based solely on combat ability - something that confirms the idea that females, being non-combatant, must be at the bottom of the pecking order. We're also told the size of their (non-goblin) slave population which turns out to be considerable, with over a hundred in a typical tribe. The number of immature individuals is double what it was previously, suggesting that they breed fast and have a high infant mortality rate. A small, but unspecified, number of goblins now have some magical ability, making the tribe a more serious threat than before.
All of this supports the "lawful" descriptor in their alignment, and their society is clearly communal. They are, as before, good at mining, but apparently have very little ability to make much in the way of material goods, beyond clothing and leatherware, somehow stealing all their weapons and tools from elsewhere. There is no mention of their love of torture, but they do kill for the pleasure of it, and will occasionally eat human flesh. They also seem to be disease resistant, living in filthy conditions and able to consume carrion without ill effects.
3EWith 3E, goblins undergo a significant change in their role, although much of the descriptive text remains very similar. Unusually, there doesn't appear to be any notable change in their appearance at all - they look just the same as they did in 2E, except that their eyes are now simply "dull", rather than "dull and gleaming", and they are significantly shorter, averaging just over three feet tall, rather than four. However, the old step-wise hierarchy of evil tribal races begins to break down in this edition, as goblins cease to be smaller versions of the combat-hungry orcs, and instead become focussed on stealth and subterfuge.
Although they are still, overall, rated as a weaker challenge than orcs, in many respects, goblins have now become their equals. Although they typically wear inferior armour, the new rules system means that their smaller size and greater agility actually make them harder to hit. They have the same hit points as orcs, and, while still strongly subterranean/nocturnal, have lost the fear of sunlight that orcs still retain. They have fully human-level intelligence, reversing things from 2E by making them the smarter of the two races, accompanied by a natural aptitude for sneaking about. The multi-lingual nature of earlier editions has, however, gone, with most goblins only being able to speak their own language.
The main weakness, compared with orcs, is that they have merely human-level strength, and, since they also use smaller weapons, therefore tend to inflict less damage on their opponents. This would, realistically, be at least somewhat offset by the greater likelihood of them striking from ambush (they seem to be good at tactics, but poor at larger scale strategy).
Beyond this, their culture seems to have changed very little. They are now much more ready to ally themselves with hobgoblins, at least temporarily. There is no mention of the females being non-combatant, with the clear implication that they are just as strong and capable as the males, while at least some tribal leaders are more valued for their cunning than for their physical prowess. In fact, craftiness and a willingness to fight dirty seem key traits in their society, something that's likely behind their shift in alignment from lawful to neutral evil; they are clearly not any kind of well-oiled fighting machine.
5EGoblins in this edition have relatively elongated skulls, projecting, pointed, noses, and exceptionally long ears. They also have a muscular build, closer to that of 1E than to the scrawny physiques of 2 and 3E, although they appear to be about the same height as in the latter edition. Despite which, they are notably weaker than their former counterparts, counterbalanced by an even higher agility, with a greater affinity for stealth and swiftly escaping from danger. They prefer scimitars to shortswords, and bows to slings, but employ the same leather armour and wooden shields as in previous versions.
While they do, in fact, have more hit points than in earlier editions, it's still a remarkably small number by the standards of 5E (only half that of orcs), marking them out as particularly puny, and emphasising that they are really only a threat in large numbers. Since they are now not just cowardly, but lazy with it, it's clear that they really rely on those numbers to achieve any kind of success in the larger world.
Socially, a few new points are made about their culture. In addition to wolves, they have also partially domesticated rats, apparently simply to use as pets. We're specifically told that females are as likely to become leaders as males (although, as is common with such races, there don't seem to be any pictures of females anywhere in the books...) Their underground lairs are said to be protected by multiple alarms and hidey-holes, and the larger tribes occupy several different ones, rather than all living communally. Goblins are once again said to love torture and "other wickedness", but on the whole seem to be regarded as a bit of a joke by the other inhabitants of their world. There's no indication in the core book that any of them can use magic.
The overall trend then, has been for goblins to become more distinct from orcs, first by emphasising the advantages of their smaller size, and then by turning them into a race that's more of a nuisance that a genuine danger. On the other hand, they have become smarter and more agile than orcs, even if they don't use this for anything much worthwhile.
There is also an increasing trend for them to be ruled over by hobgoblins; in 1E, there is (initially) no indication that they are even related, and, by 5E, a high proportion of goblin tribes have hobgoblin masters. In some settings, such as Eberron, pretty much all goblins live under hobgoblin dominion, with all the great tribes being of mixed race. In Mystara, while goblins are more likely to be independent, a number do live under hobgoblin rule, and the two races are able to cross-breed.
In Forgotten Realms, the default setting of modern D&D, goblins are regularly enslaved by hobgoblins, who use them as skirmishers and scouts, keeping even their leaders in menial and subservient roles. Where goblins are free from their larger kin, they have a stratified caste-based society that leans towards the lawful - their continual infighting is probably what prevents it from actually being described as such. They are also, as humanoids tend to be in FR, very religious, although this is more accurately described as a sort of superstitious dread, since they are more terrified of their deity than anything else, and don't seem to have clerics. Volo's Guide does reveal that they do, in fact, have some spellcasters, but that they are relatively weak, and always small in number.
The goblins of Pathfinder look quite different from their D&D inspiration; they have greenish skin, long ears, and disproportionately large heads that look as if they might almost snap their necks. They are even more agile than the 3E sort, but are otherwise fairly similar. Some notable points about their culture include the fact they have a particular hatred for gnomes, but not especially for dwarves, and that they now actually prefer to eat the flesh of humans and similar races - this was not mentioned in 3E, and was said to be an unusual occurrence in 2E.
Modelling D&D goblins in other game systems depends somewhat on the exact vision of the race that you have, based on its variations down the years. In general though, they are physically weaker, but more agile, than humans, and probably have some natural Stealth skill or the like. Their intelligence varies, as does their constitution/endurance (or equivalent); the latter may be balanced by some limited disease resistance if it's otherwise low. If Cowardice is a specific trait, they likely have it, and they typically seem to be sadists, too. Their combat ability is typically portrayed as rather low, but, in many other systems, their low strength alone may be sufficient reason for that.