Re: Probably a question for http://what-if.xkcd.com/
They use tidal forces --- the station's big enough that the Dragon is nowhere near its centre of gravity, but is being carried along in the same orbit as the station because it's physically attached. This means that when they let go it'll naturally follow a non-trivially different orbit. The result, seen from the station's perspective, is that the Dragon will slowly fall away.
They use this effect when undocking to get vehicles far enough away from the station that they can safely use their thrusters. They also use it when docking --- it mean you get a natural braking force for approaching vehicles (along a particular vector), which is dead handy as it means you don't need to fire your thrusters towards the station.
Physics is awesome; and you can simulate this in Kerbal Space Program if you want to try it for yourself. Just make sure your two vehicles are lined up along a planetary radius.