The Naquadria reactor core was a hyperdrive generator installed on the Prometheus as Earth's "shortcut" to interstellar travel. Powered by the element Naquadria, a buffer was installed to prevent the reactor from going critical due to naquadria's inherent instability. (SG1: "Prometheus", "Unnatural Selection")
However, during the shakedown cruise, the Prometheus passed through a massive gravity wave from a collapsing star, while it was in hyperspace, which severely damaged the reactor's buffer. In order to fix it, Prometheus made a brief hyperspace jump to the closest planet with a Stargate. This, however, overloaded the hyperdrive engines and forced the crew to eject the reactor into space before it went critical. When it eventually overloaded, the EMP energy from the reactor core greatly damaged the Prometheus despite the ship having Asgard shields which ultimately stranded the ship on an alien world until a replacement could be procured. (SG1: "Memento")
Asgard technology has recently made this technology obsolete as current Asgard hyperdrives (which were gifted by the Asgard to the Tau'ri) are capable of propelling ships at speeds far greater than that achieved by naquadria-fueled reactors. (SG1: "Unending")