The Rat King was originally the Slayer, a prototype bio-mechanical super soldier created by Agent Bishop using DNA from aliens, the Turtles, himself and Splinter. The Slayer was meant to be used to fight off alien threats, and was given a test run against the Turtles, who broke into Bishop's laboratory looking for the kidnapped Splinter. The Slayer was presumed dead when Agent Bishop's lab was flooded during a fight with the Turtles and Splinter.
In actuality, the Slayer survived and was sent hurtling through the sewers, eventually being deposited near a ruined industrial complex. Losing several of his cybernetic parts, cloaking device and healing ability, the Slayer degenerated into an even more monstrous form, becoming the Rat King, as the rats don't fear him.
The Turtles ran afoul of the Rat King when they and Casey were doing stealth exercises in the industrial complex. He captured Michelangelo and attempted to feed him to the rats, and eventually revealed himself to his foes. After the Turtles and Casey were able to drive back the army of rats, he was enraged and leaped down to fight them himself. He eventually found himself in single combat with Leonardo, and was thrown down into the rats, where he was once more presumed dead. However, he had survived yet again, and retained his ability to control the rodents.
Back to the Sewer
It appears that by this time he had somehow recovered his healing, as his body was practically whole save for the cybernetic parts.
The Rat King has the ability to control rats telepathically, which allows him to direct them at his enemies. It is not explained why he has this power, but presumably it is related to his mutated rat DNA.