Hyperdrives are devices which allow ships to break the light-speed barrier, enabling interstellar and in some cases intergalactic travel. They function by taking the vessel into hyperspace, where normal physical laws that would prevent faster-than-light travel do not apply.
A hyperdrive allows a vessel to open a subspace window and move into hyperspace. In this manner, a ship can cross vast distances without experiencing relativity. Hyperdrives vary in their effectiveness from race to race, with some being much faster than others; most hyperdrives are designed to travel within a single galaxy, while more advanced models can travel between galaxies in the same amount of time.
The effectiveness of a hyperdrive depends on two factors: design and power input. Given enough power, a hyperdrive can be made to go far faster than it would normally be capable. The design of a hyperdrive is what allows it to make use of the power it's given effectively. A Aurora-class battleship, even with a ZPM, cannot match the speed of a fully-powered Atlantis' Stardrive (three ZPMs), which can cross the same distance as Aurora-class battleship in a fraction of the time.