The other dimension of the Phantom Zone was discovered by Kryptonian Scientist Jor-El. He invented a device that would transport people to the zone as a method of imprisoning criminals. The criminals originally were punished by being sealed into capsules and rocketed into orbit in suspended animation with crystals attached to their foreheads to slowly erase their criminal tendencies. This practice was abolished in favour of the Phantom Zone, which was considered a more humane form of punishment.
The Phantom Zoners exist in a featureless non-corporeal state and can observe, but cannot interact with, the regular universe. Phantom Zoners do not age or require sustenance in the Phantom Zone. Phantom Zoners were able to survive the destruction of Krypton and focus their attention on Earth, as most of the surviving Kryptonians now reside there. The Phantom Zoners particular grudge against Superman because his father created their eternal prison.
When they manage to escape, they usually engage in random destruction, particularly easy to them since, on Earth, each has the same powers of Superman. Nevertheless, Superman periodically released Phantom Zoners whose original sentences had been completed, and these fortunately tended to be relatively repentant criminals.