The Dark Crystal was made in the era between traditionally-animated feature films and later movies produced by computer-generated techniques. All characters in the movie are muppets, and none are based on humans or any other particular creature. The movie makes an attempt to study the nature of good and evil in terms of conscience, vital drive, and harmony.
Warning: Wikipedia contains spoilers.
One thousand years before, "the crystal cracked" and separated godlike beings called Urskeks into hunchbacked, gentle orange beings known as Mystics and vulturelike, cruel bipedal beings known as Skeksis. The Skeksis drove the Mystics from the castle where the now-shattered crystal resided and instituted a reign of terror over their world. Their wrath is particularly directed toward the elf-like Gelflings due to a prophecy that promises the restoration of the crystal and the end of the Skeksis' power. The prophecy, rediscovered in an ancient Gelfling city, reads like this:
When single shines the triple sun, What was sundered and undone Shall be whole, the two made one, By Gelfling hand, or else by none.Jen is the last (he believes) of the Gelflings. After his parents were killed by the crustacean-like Garthim created by the Skeksis, he is raised in a lush valley the mystics reside in. The Mystic who has raised him is dying, and he calls Jen to his side and reveals that he is meant to "heal" the crystal by replacing the shard at Aughra's observatory. The emperor of the Skeksis dies as the same time the mystic does because they are both part of the same being. In a duel over the succession called Haakskeekah, the chamberlain Skektek is driven from the palace in rags.
Jen reaches Aughra, a short purple furry female, and discovers the actual crystal shard by playing music which it resonates to. He must put the shard back in the crystal in time for the Great Conjunction, when his world's three sun will be lined up with one another. Garthim arrive to capture or kill Jen, who flees as Aughra is taken prisoner. By a river, Jen is frightened by a ball-shaped pet known as Fizzgig and meets another Gelfling, Kira, that he never knew existed. They stay for a night among the bulbous Pod People who raised Kira and are then attacked by Garthim there. In frustration and despair, Jen throws the crystal shard away.
Next they arrive at the old Gelfling City, where Jen reads the prophecy about the crystal. Jen and Kira are confronted by the disgraced Skektek, who offers to help them, but they refuse because of the Skeksis' extermination of Gelflings. Riding furry, longarmed Landstriders, the Gelflings soon catch up to the Garthim that attacked Kira's village and try to free the Pod People. Although they fail, Jen and Kira end up at the Teeth of the Skreesh, the undefended entrance to the castle. Skektek meets them again and takes Kira prisoner while burying Jen alive in a cave-in.
The Mystics begin their trek to the crystal castle while Skektek is restored to his position as chamberlain. The Skeksis still need a Gelfling to make their "everlasting essence", a potion with which their leader Skekung the Garthim-Master will regain his youth, by draining Kira's life essence. She calls out to the imprisoned animals in the lab, who break free and kill the Skeksis overseer (and his Mystic counterpart dies at the same time). She escapes, and the link between her and Jen gives him the strength to escape the cave-in.
In the central chamber where the crystal's kept, Jen jumps onto the crystal himself but loses the shard. Kira throws it back to him, but she's killed by a Skeksis. Jen plunges the shard into the crystal, shattering the Garthim (who were originally created by the Skeksis, so they're not living beings) and reuniting the Mystics and Skeksis into their Urskek incarnations. One of them restores Kira to life, and they leave this plane of existence since the crystal has been healed.