An alternate dimension
discovered by Superman
's father Jor-El
In the waning years of Krypton's existance, Jor-El, one of Krypton's leading scientists, discovered an alternate dimension. Traveling there by means of a projector of his own design, Jor-El discovered this dimension was a nightmare world of perpetual twilight, where the inhabitants lived as wraiths, seeing our dimension, but unable to interact with it. Rescued from there by his wife, Lara, Jor-El dubbed this dimension the Phantom Zone.
The Kryptonian government decided to use Jor-El's discovery to deal with some of its more dangerous criminals and prison overcrowding. Up until this point, these criminals had been placed in suspended animation aboard satellites circling Krypton. Rather than maintain these capsules, the Kryptonian government decided to place these criminals in the Phantom Zone to serve out their time.
With the destruction of Krypton, the criminals of the Phantom Zone were trapped there, never aging. They were eventually freed when Superman rediscovered the means to access the Phantom Zone, through his father's invention. Because of their ability to see into our dimension, the Phantom Zone villains knew Superman's secret identity, making them extremely dangerous to him.