The Warp Drive relies on the Alcubierre Drive theory of expanding and contracting space-time in a bubble around the ship. The Warp Drive uses hundreds of thousands of Casimir Nano Plates to create a negative energy density without the use of exotic matter. It then uses power from a very large fusion drive to alter space-time with the negative vacuum energy. Both the Casimir effect and the Alcubierre metric have been known to science since the 20th century.
Over the course of the next few millennia, the technology improved, increasing the "speed" of the drive in increments so that eventually it would only take a half year to go from one edge of the galaxy to the other. The Warp Drive was rendered obsolete when the ability to create wormholes was discovered, but ships were still outfitted with them and the technology has continuously been improved upon since then.