Here is a fairly thorough background in terms of theories in regards to the video to help get you up to speed (no pun intended!)

The physics of spacetime described by Einstein’s Theory of General Relativity allows spacetime to become warped due to the relationship between matter/energy density and the gravitational field described by the Einstein Field Equations, in the most general form Ruv – (guvR)/2 + guv = (8pG/c4)Tuv, which equates that matter and energy found in the large scale structure of the universe creates a positive torsion in spacetime, causing the warping of spacetime which is associated with the strength of the gravitational force.

The warp drive proposed by Alcubierre could achieve near light speeds and even faster-than-light speeds by distorting space-time. To accomplish this, a theoretical device would generate a field of negative energy that would squeeze or stretch space-time, creating the bubble. The bubble would ride the distortions like a surfer on a wave.

The best part of this video is that they have many incredible minds using different examples to illustrate parts of this controversial subject.  Scientists, engineers and awesome theorists!