The Casimir Pump is a completely fictional device. It exploits the Casimir Effect which has been demonstrated and speculates that the positive and negative energy can be segregated using a diode analog. Once you have a "pool" of negative energy, many things become possible or so we assume.
Where negative energy exists, it is postulated that space does not exist. Thus the Casimir Pump can create tiny regions of "not-space" which are called "pinch point transits" or PPTs in the book. At very close range, within a gravity well, the region of not-space collapses very quickly. The only thing preventing this is linking to a kindred region of negative energy, called a resonance. Thus PPT resonance is the basis of the telepathic communication between Vuduri and created the Overmind.
A starship uses PPT generators to create much larger pools of negative energy. These pools of negative energy are used to punch through the "fabric" of space, collapsing it and creating PPT tunnels. Thus a spaceship that travels through the PPT tunnel can, mathematically, go faster than light because it travels a certain distance in zero time.
Segregating the negative energy leaves a pool of positive energy. This is used in a variety of ways such as creating elementary particles or accelerating these elementary particles thus forming the plasma drive. It can also be converted to a more universal form such as electricity.
Here is Rei's comment when OMCOM explained this to him: “So, let me get this straight. You go to a region where there is no energy. You suck negative energy out of it and get to go faster than light and the waste product is power that you use to drive your ships? That’s…that’s beyond perpetual motion. That’s impossible."
Impossible? Maybe. But it makes for a good technological basis for many elements of the story.