The Setting

The film takes place on "another world, another time... in the age of wonder". The setting is Thra, a biodiverse planet featuring creatures, environments, and magic. Thra has three suns; tthe Great Sun, the Rose Sun, and the Dying Sun. Many creatures and races inhabit the planet, but the dominant race is the urSkeks, who came from another world and are the guardians of the Crystal of Truth. The Crystal harnesses the forces of nature, especially the light of the three suns, for the benefit of all inhabitants of Thra.

One thousand years before the beginning of the movie, during the Great Conjunction of the three suns, the urSkeks cracked the Crystal of Truth, and split into two races; the hunchbacked, gentle beings known as urRu or "Mystics" and the vulture-like tyrants known as Skeksis. In that moment the Crystal became the Dark Crystal. The Skeksis then drove the urRu from the castle where the cracked crystal resided and instituted a reign of terror and control over their world. Their wrath was particularly directed toward the elf-like Gelflings, due to a propecy that foretold the restoration of the crystal and the end of the Skeksis' power. The prophecy, rediscovered in an ancient Gelfling city, read as follows....

urSkeks

The urRu / Mystics

These creatures were benevolent, hunchbacked counterparts of the Skeksis. The urRu have four arms, elongated heads, white hair and tails. The urRu look similar to the Skeksis in body shape and also in that they were gnarled with age; yet the urRu were very wise and in tune with nature, hence their longevity and also their title of "Mystics". They often performed enigmatic rituals which has also given them the title of "chanters". There were ten urRu at the beginning of the film who included....

urSu the Master
urZah the Ritual-Guardian
urIm the Healer
urSol the Chanter
urTil the Alchemist
urAmaj the Cook
urNol the Herbalist
urAc the Scribe
urYod the Numerologist
urUtt the Weaver

Skeksis

The Skeksis are essentially the ten "evil" versions of the ten "good" urRu. The word "Skeksis" serves as both singular and plural form for this species. Like their urRu counterparts, they have four arms; but in the Skeksis the two lower arms had become weak and atrophied, and are rarely seen within the movie. The Skeksis had kept themselves from dying of old age by draining the vitality from other beings, yet remain hideous in appearance.  Jim Henson, who created the puppets, had said that in the development of the Skeksis, the creators drew inspiration from the seven deadly sins, in that each Skeksis represents a different kind of evil, such as cruelty, selfishness, greed, unchecked ambition, treachery, and wrath. The Skeksis included....

skekSo, the Emperor
skekZok the Ritual-Master/High Priest
skekUng the Garthim-Master/General and later the new Emperor
skekSil the Chamberlain
skekTek the Scientist
skekAyuk the Gourmand
skekNa, the Slave-Master
skekOk the Scroll-Keeper
skekShod the Treasurer
skekEkt the Ornamentalist

UrSkeks

The UrSkeks are the original species of which the urRu and the Skeksis are derived. The UrSkeks are the "whole" of the their urRu and Skeksis halves coming together, although implied to be greater than the sum of their parts. The UrSkeks are seen at the end of the film when the Dark Crystal is made whole again by the Gelfling, where they are depicted as tall, luminescent beings of vaguely Gelfling-like shape. They sported large craniums and slim bodies. Only eight appeared in the end of the movie, with UngIm as their representative. They include:

UngIm: General/Garthim-Master skekUng + Healer urIm
SilSol: Chamberlain skekSil + Chanter urSol
ZokZah: High Priest/Ritual-Master skekZok + Ritual-Guardian urZah
AyukAmaj: Gourmand skekAyuk + Cook urAmaj
NaNol: Slave Master skekNa + Herbalist urNol
OkAc: Historian skekOk + Scribe urAc
ShodYod: Treasurer skekShod + Numerologist urYod
EktUtt: Ornamentalist skekEkt + Weaver urUtt

Two more UrSkeks were mentioned but did not appear, due to the deaths of their UrRu and Skesis counterparts:

SoSu: Emperor skekSo + Master urSu
TekTil: Scientist skekTek + Alchemist urTil

According to The World of The Dark Crystal, the UrSkeks originated on a world where moral imperfections were found intolerable. The UrSkeks, of which there were originally 18 led by SoSu, were banished from their homeworld and entered the world of Thra via a portal opened by the shining of the three suns on the Crystal of Truth. There, they encountered Aughra, who had been badly burned by the intense heat given off by her close proximity to the Conjunction. They healed her and together made exchanges of knowledge; Aughra teaching them the ways of the planet's nature and ecology while the UrSkeks taught her astronomy. They hollowed out the mountain containing the crystal that brought them to the world and created a magnificent castle. Thereafter the UrSkeks sought to rectify what they had been taught to believe their curse of self-impurity.

Creating a network of mirrors around the crystal, the UrSkeks sought to trap the light of the next great conjunction to burn out the imperfections on their souls. For another thousand years they waited till finally it arrived. Upon entering the light, rather than being cleansed, the UrSkeks were splintered into separate species; the Skeksis, commanded by SkekSo, and the urRu led by urSu. A fight broke out, resulting in the crystal receiving a blow, which chipped off a shard. The shard disappeared and the UrRu left the castle to the Skeksis.

Despite the separation, there was still a sympathetic bond between each Skeksis and its urRu counterpart, a constant reminder that they were only halves of the same being. If either is wounded, the other feels the pain and suffers an identical injury. If one dies, both die in the same manner, preventing the feasibility of war. Within the movie only ten Skeksis/UrRu pairs remained. When the story begins, both skekSo & urSu perish, leaving skekUng & urIm to succeed them respectively. By the upcoming conjunction, the process that created the two races was reversed and the UrSkeks were reformed. Their new leader, UngIm, revived Kira before the UrSkeks departed into a higher level of existence and left the Gelflings as the keepers of the Crystal. Because skekTek was killed during the course of the film, destroying his urRu counterpart urTil, the UrSkek 'TekTil' never appeared