Hyperspace cores are devices that allow starships to traverse interstellar distances within short periods of time.
The Kushan used a hyperspace core contained within one of the original prison ships that brought them to the planet Kharak. The hyperspace core, which formed a crucial portion of the Kushan mothership project, was fitted with new containment units and installed into the Kushan Mothership. This hyperspace core eventually allowed the Kushan to flee Kharak and journey into the heart of the galaxy.
Main article: Three Hyperspace Cores
In Homeworld 2, Far Jump Cores are revealed to be artifacts from an ancient time, three of which exist and were believed to be created by Sajuuk, the galaxy's mythological Creator figure. These Cores allowed 'Far Jumping', an ability characterized by the capability to cross long distances rapidly.
The First Core was discovered by the Bentusi, who set up trading routes and made contact with many galactic civilizations. The Second Core was discovered by the ancient Hiigarans, ancestors of the Kushan, and used to wage war against the rival Taiidan Empire. After this war ended disastrously for the Hiigarans, the Hiigarans were forced to resettle at the edge of the galaxy. They, however, secretly took their Core with them as they traveled to Kharak. This core was the core used as the heart of the Mothership.
The Third Core was discovered by a messianic Vaygr warlord named Makaan, who set out to locate the other two cores and waged war against the new Hiigaran empire. Makaan was eventually killed, and the Three Cores were united to re-activate Sajuuk (which took the form of an ancient, derelict spacecraft), allowing the Hiigaran leader Karan S'jet to ascend to the form of the Sajuuk-Khar, the 'chosen of Sajuuk'. S'jet then proceeded to use Sajuuk to save Hiigara from the Planet Killers, three ancient weapons of mass destruction unleashed by Makaan and the Vaygr.
After the planet killers were destroyed, Sajuuk was revealed to be the key to opening a vast network of hyperspace tunnels, opening up the distant galaxy for the Hiigarans to explore.