To simplify, the same way that a surfer on the sea can use the movement of the sea itself (waves) to surf!
An Alcubierre drive (they're theoretical) would basically constantly compress the time curve of spacetime in front of the craft, allowing the craft to "ride" this compression as it moves forward, which means that the local speed of light of the craft is faster than the speed of light of an external observer. Note that the main issue we have is to find something that can compress space, and then to have it have enough energy for it not to be trivial (because 110% of the speed of light, while technically FTL speed, is still very slow for interstellar travel). And of course, while the existence of something that does this spacetime curve compression fits the math we have, we've yet to find a material or technique that actually does so.