The intergalactic drive was a theoretical piece of technology allowing easy travel over the distances between one galaxy and another.
The Federation did not appear to have intergalactic drive technology but Avon implied it was being worked on. The Andromedan aliens who attacked the Federation in the Intergalactic War presumably had the drive fitted to their invasion fleet. (B: Star One)
In "Horizon (episode)" Ro states that monopasium 239 is needed for the "hyperspace ships".