The Phantom Drive is a Kryptonian engine that is capable of accessing black holes by folding space as Kal-El indicated to travel vast distances across the universe almost instantly by passing through the Phantom Zone.
Jor-El built his own Phantom Drive for a small spacecraft designed to carry his newborn son Kal-El away from Krypton's impending destruction. The Phantom Drive was programmed to open a portal to another solar system, namely that of the planet Earth.
After General Zod and his insurgents failed in their attempt to take over Krypton, they were placed in the Phantom Zone. When Krypton exploded, the planet's explosion released their prison ship, the Black Zero, from the Phantom Zone. Adrift in space, Zod and his cohorts retrofitted the Phantom Zone Projector by taking the Phantom Drive and installing it on their ship as a means to travel the universe looking for other surviving Kryptonians.
Thirty-three years after Krypton's desctruction, Zod and his men discovered that Kal-El and the Growth Codex were on Earth; they then traveled to the blue planet, intending to recreate Krypton there. With Kal-El unwilling to give up the Codex or his adopted homeworld, Zod and his followers began to terraform Earth using a World Engine and the Black Zero, powered by the Phantom Drive. The US Military used Kal-El's ship as a makeshift bomb and crashed it into the Black Zero, causing the two Phantom Drives to create a temporary portal that sucked both ships and everyone within the proximity into the Phantom Zone including anything that has passed through the Phantom Zone or traveled via a Phantom Drive.