Stability: The ability of the body to remain unchanged or aligned in the presence of external forces or changes.
Mobility: The ability of the body to perform movement.
These two words are the key to developing a proper golf swing.  During the golf swing your body is continually changing from a stable joint to a mobile joint.  These changes are what help provide the mechanics for the best golf swing.  Stability and Mobility can also be classified as strength and flexibility, which is why making sure you are both strong and flexible will not only improve your golf swing and score, but will also lessen the likely hood of injury.
An exercise to improve strength and flexibility:
The lunge stance with rotation is one of many exercises that can be performed using cable machines.  In this exercise, instability is created with a lunge stance, and trying to maintain that position while performing trunk mobility helps improve stability.  If you don’t have the stability to get into a lunge stance immediately, start by putting your feet into a wide squat stance and work yourself into the lunge position.  Check this link for a video of the movement.