Demons are a faction in the Dark Souls universe.
When the Witch of Izalith tried to use her powers to recreate the First Flame, the primordial source of life and diversity, she only sparked an uncontrollable surge of corrupted energy known as the Flame of Chaos. As a twisted imitation of the First Flame, the Flame of Chaos could not create anything but only warp existing beings, thus perverting all life in its wake: starting from the Witch of Izalith and her children, the Flame of Chaos transformed its victims into monsters that exhibited various traits of different creatures (like the Capra Demon, almost humanoid aside from its caprine skull and its four burning eyes) or unrelated species (the Witch of Izalith herself became the Bed of Chaos, an entity composed by a skeletal headless torso and an insectoid "core" and both were made of desiccated branches) and even imparting a semblance of life to inanimate matter (the Titanite Demons).
Most demons in Dark Souls have demonstrated to be intelligent enough to craft their own equipment using archtree wood, titanite and demon bones, and none of them ever used weapons forged by other races. Despite their blasphemous birth and hideous appearance, the Demons had some sort of alliance with the Gods themselves. It is not known if there was a real agreement sealed due to the common hatred towards the Undeads (both Demons and Gods are born from fire, even if in different ways, while humans are closer to the Abyss through the Dark Soul itself) or if it was just a truce in the name of the Witch of Izalith (who, prior to becoming the Bed of Chaos, was one of the Lords alongside Gwyn and Nito), but it is possible to see this accord in various locations: not only the Undead Asylum, guarded by the Asylum Demon and a greater Taurus Demon but even Anor Londo -the city of the Gods- is home for the Crow Demons (trapped within the Painted World of Ariamis alongside everything belonging to their patron, the goddess Velka) and for the Batwing Demons. The latter are not only tasked with the transportation of the Chosen Undead between Sen's Fortress and Anor Londo, but also use lightning weapons similar to the Silver Knights' spears, thus hinting that they helped to protect the city against Dragons: a logical but disturbing explanation for the unique appearance (extremely pale, lanky and able to manipulate lightning weapons) and residence of the Batwing Demons is that they were once Godkin, like the Silver Knights.
The Sanctuary Guardian and the Gargoyles are hinted as Demon-related beings, not born from the Chaos Flame but created through magical or alchemical means, since they have mixed features that nevertheless seem to have been chosen for specific purposes (the Belfry Gargoyles that protect the Bell of Awakening from the Undeads are able to breath fire, while the Sanctuary Guardian of Oolacile and the Gargoyles of Anor Londo -cities at war with the Dragons' kin- can breath lightning). The Centipede Demon too was not created by the Chaos Flame, at least not directly: this mismatched hybrid of insect, canine and humanoid came into existence by accident, when a careless child foolishly dropped his enchanted ring onto the bedrock of Izalith.
Even if not officially called "demons", there are three species that nevertheless belong to this race: the Cragspiders not only have a misshapen body with spider legs and fly wings but also dozen of beady eyes (like Quelaag's lower body) and humanoid arms complete with five-fingered hands, plus they can breath fire (an element that normal monsters fear); the Chaos Eaters are even more alien in appearance, sporting six trunk-like appendages that act both as arms and as acid sprayers while their cylindrical body, vaguely reminiscent of a sea anemone, has a gaping maw on the top and is dotted by almost-human eyes that never stop rolling and scanning the surroundings. The Parasitic Wall Hugger is a unique being but its strange appearance (eight insectoid legs attached to a slimy worm body, centered around a small mouth like that of a starfish) and its presence in Blighttown hint that it is some kind of Demon.
Dark Souls II
It is known that the Flame of Chaos, called The Old Chaos, birthed horrible beings that were battled by the Ivory King and his Knights of Eleum Loyce. Even if none of them returned alive, the utter absence of any of the Fire Ages' Demon could mean that the King's army managed to slew all of them before succumbing to the foul Chaos. The being called "Demons" encountered by the Bearer of the Curse did not have an evident connection to Chaos, instead they came in existence when powerful souls begin to fester with corruption: the Covetous Demon was once a man who started to gorge himself after Mytha broke his heart, the Demon of Song was a monster which craved the taste of human flesh and the Smelter Demon was formed when an iron construct engulfed the Iron King's soul. Three possible exceptions are the Iron King (who became a demonic monster when something below his domain, amidst the "fire that rose from earth", possessed him), Lord Aldia (through countless experiments he discovered an unspeakable truth, thus becoming an entity made of fire and dried branches similar to the Bed of Chaos) and the Flame Salamanders (strange reptilian monsters with fire powers). The Gargoyles are called "Stone statues that mysteriously came to life" thus explaining that, despite their real beastly appearance, they were once non-animated objects just like the Titanite Demon.
Dark Souls III
In the third known cycle the Flame of Chaos had not survived, making the ancient Demons a dying race. The ruins of Izalith are littered with huge pile of corpses of ancient Demons, most of them belonging to lesser Capra Demons and Taurus Demons, while few surviving specimens roams aimlessly a world that has no place for them: these beings, called Stray Demons, look like their ancestors only superficially since their body is smaller and made mostly by rock, wood and lava (much like the Bed of Chaos). It must be noted that the Batwing Demons, a lesser breed of ancient Demons, were unfazed by the Chaos Flame's extinction and kept their duty as "ferrymen" for the ones that will follow the legacy of Gwyn (thus proving a deep connection between their kin and the Gods). The Ghru are a new kind of Demon that came into existence when the corruption of the swamp of Farron Keep warped its human inhabitants: they sport mainly caprine and avian features but the elder individuals have body and fur reminiscent of ancient Dragons. A special mention goes to the Gargoyles of this cycle which are born not from the Chaos Flame nor from an accurate sorcery, but from the Profaned Flame: this aberrant energy did not imbued their stone body with a realistic living appearance, thus making them more like coarse stone carvings much like the Demon Statues, with vaguely chiseled details, short skeletal tails and pauldron-like wings sturdy enough to act as shields but nevertheless able to fly (probably through some sorcery woven into their stone bodies); most of them were headless but the most powerful individuals sported a disturbingly realistic humanoid skull on top of their misshapen body.
Demons and Humanity
It seems that the flawed nature of the Chaos Flame created some kind of link between the two antagonistic concepts of "light" (the energy manipulated by the Gods and the Fire itself) and "darkness" (every shard of humanity and the Abyss). First, it is possible to trace this link to Chaos weapons: these instruments are imbued with raw Fire but their power scales with humanity like an Abyss-tainted weapon. Another sign of this bizarre duality is Quelaag's sister, a Demon known as the Fair Lady. This compassionate being attempted heroically to stop a great calamity, a great tide of toxins created by an uncaring pyromancer, thus becoming extremely weakened, blind and almost catatonic: only feeding her humanities makes her regain a bit of strength. The third, and perhaps most evident hint of the warping nature of Chaos are the Taurus Demon and the Capra Demon: these two species carry humanities, thus they were probably human in origin.