.. nothing but Science fiction speculation could be done with that subject.
My two cents.
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I would figure its some kind of warp drive that encapsulates the ship is a pocket of spacetime, The ships reference frame is placed inside of a bubble and its the bubble itself that moves at FTL speeds.
Einstein said that Mass cannot move faster than the speed of light but that Space itself can, so the space is moving at superluminal speeds while the ship inside it (as far as it is concerned... is stationary) and so its not breaking any physical rules.
The jump between stars, could be some form of higher dimensional travel where the 4d bubble that your ship is inside of is pushed upwards to a plane that houses more than the 3 spacial dimentions and 1 of time that we are used to here in normal space. With extra dimensions available within the flow of time and shortcuts through space that are beyond a straight line the ship can displace its frame in spacetime and place it somewhere else in the galaxy.
The star we jump to is a mass target. Einstein once said that gravity as we see it in this universe is just the tail of the lion, by this he meant that we see only a small part of the entire force of gravity and that behind the curtain maybe in other dimensions, gravity is at full force and the rest of lion is hiding. Maybe the gravity of stars is much stronger and easier to detect at long distances in witch space and can be used to pull your bubble of spacetime through witch space towards the source. We fall towards stars in witch space.
