Once a powerful ruler, The Goblin King kept watch over his land, the labyrinth on it along with the city surrounding his palace in the center. He was the one young selfish girls called upon when they felt like a slave to their young siblings. If the girl felt remorseful, The King would give her a choice, 13 hours in which to solve his labyrinth or forget the baby. Most tried but failed.
Until her, Sarah Williams. 15 years old, dark hair, green eyes and clever wits. She wished her young brother away like many had before, Jareth gave her the same choices as all the others, but this time the outcome was very different.
After his defeat, Jareth fell into a depression, leading to the loss of his kingdom and then his own life.
Long Live the King
In a time long long ago a sorcerer named Jareth fell in love with a girl named Sarah. Sarahs father and step-mother would not let her marry Jareth because they wanted her to keep her, as a servant, to care for their other child. In a fit of rage Jareth kidnapped this other child and spirited it away to the fairy world. In this new world Jareth built a palace for his Sarah. He turned the spoiled child into a goblin, and kept it to be a servant.
Many stories of the fairy world tell us that time moves differently there than in our world (Rip Van Winkle for one). In the time it took for Jareth to build his kingdom, which he may have thought was little more than a few years, Sarah grew old and died.
Overcome by grief and addled by a lifetime spent in a strange world filled with monsters, Jareth goes mad. He refuses to believe that he has lost his love. He searches the mortal world from his castle, looking for her.
Sarah is Hebrew name. So, it is common, and has been in use for thousands and thousands of years. It does not take long (for him) to find a dark haired girl named Sarah, who has a younger sibling, and who feels that she is treated unfairly by her step mother. In a fit of rage he kidnaps this other child and spirits it away to the fairy world. Perhaps this new Sarah dies in the quest to find the child, perhaps she wins her sibling back and flees.
This is how Jareth becomes the goblin king. Every goblin in the goblin city is a child Jareth has stolen, who was not recovered by a Sarah... This is why he builds the maze.