If you imagine space as a flat rubber sheet, the warp drive allows you to essentially warp space downhill in front of you and uphill behind you, allowing you to accelerate past the speed of light as its imposed over a flat plane.(Not literally of course, but if we're sticking with the inherently false "flat rubber sheet" model, than it kind of fits)
You still technically don't go faster than light in the space you occupy, its that the space you occupy itself is warping in front and behind you, allowing you to accelerate past light speed relative to the rest of the galaxy
Thats not...exactly right, as it were, but its a decent explanation, I think.
In fact, now that I think about it, the actual acceleration inside the warp bubble has to be next to non-existent. Otherwise, you would have to deal with all the problems that relativity brings.
