Movement of the arm requires joint mobility and muscular stability. Moving the arm requires appropriate muscle facilitation and mobility in the shoulder joint, the scapulo-thoracic joint (which is not a "true" joint, more of a physiological joint), the acromioclavicular joint (AC) and the sternoclavicular joint (this is the only joint connecting the arm to the axial skeleton).
Take a look at the pics on the left. There are a lot of muscles that can affect the movement of the arm, the scapula, the shoulder, and the clavicle. So... basically what I am pointing out here is that optimal muscle function of the shoulder girdle is key to a healthy pain free shoulder joint, neck and arm.  
Muscle, bone and connective tissue adapt to how we use them.  And typically during a day our arms are positioned out in front of the body: computing, driving, pushing a stroller/walker/cart. This positioning, along with all of our other daily habits of grasping, clenching and tensing can lead to shortened muscles, winged shoulder blades and internal rotation of the shoulder joint which can lead to impingement and eventual rotator cuff tendonitis/tear.

Before we get to the stretch, observe the position of your shoulder blades when your arms are down by your side.  Notice the medial edge and the lower angle.  Do they wing away from your back like mine?  Ideally the scapulae should be positioned equidistant from each other with no visual boney edges.  Winging of the scapulae is an indication of muscle imbalance.

Just for fun, see how you need to move your scapulae so you don't see your boney edges poking away from your thorax.  In this pic you can see that I had to move my blades forward and elevated a little.  Once the blades are in the ideal position you can really see some of the culprits driving this imbalance:  can you say tight pectorals anyone?

Now for the stretch.  Bring the hand behind the back.  Make sure to keep your elbow straight down from your shoulder (notice how this makes me wing even more.  More than likely this will happen with you too).  Begin to bend the elbow as if to reach for your opposite shoulder blade.  Notice your elbow, did it start to go out wide?  If it did, you went too far.  Bring your arm back down so you can comfortably hold in position in a gentle stretch.  Believe me, this can be intense, don't let it. Hold for up to a minute.

Now, let's refine the stretch.  You will need to have a mirror for this so you can see the position of your shoulder blade.
Bring your hand behind your back.  Move your scapula (usually forward and up) so that you do not see winging anymore.  Make sure to watch your elbow.  In this pic you can see that my elbow moved outward a little bit, and is not straight down from my shoulder.  The requirement or alignment marker for this stretch is to keep the elbow in line with the shoulder.  To correct that, I would need to lower my hand so the stretch isn't so intense.  Notice in the pic that the lower angle is still lifted away a little bit.  But because of my tension, I wasn't able to get completely flush with my thorax without moving my elbow.