The concept of the Warp Drive was initially a speculative idea based on a solution of Einstein's field equations in general relativity as proposed by Mexican theoretical physicist Miguel Alcubierre, by which a spacecraft could achieve apparent FTL if a configurable energy-density field lower than that of vacuum (that is, negative mass) could be created.
Rather than exceeding the speed of light within a local reference frame, a spacecraft would traverse distances by contracting space in front of it and expanding space behind it, resulting in effective FTL. Objects cannot accelerate to the speed of light within normal spacetime; instead, the Alcubierre drive shifts space around an object so that the object would arrive at its destination faster than light would in normal space without breaking any physical laws.
Initially, this form of FTL was considered to be impossible until a prototype vessel called the IXS Enterprise.was constructed in 2059. Since then humanity has been exploring and spreading throughout the Milky Way galaxy. The earliest renditions of Warp Drive could only travel at very slow "speeds", making a journey to Earth's nearest star, Proxima Centauri, over half a year long. It also needed massive fusion reactors the size of a couple city blocks just to operate. By the year 3015 Warp Drives capable of 2000C, or 2000 Light years a year, were commonplace.
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 despite having been rendered obsolete.
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.