The two dogs in these pictures nicely illustrate one who is following the obedience command "Down" but still very tense and ready to break the command at the slightest distraction and the other has learned that Down actually means lie down and relax. Easily the biggest breakthrough I had before becoming a dog trainer was understanding that my dog, Oliver, was a nervous, anxious dog. That thought never occurred to me. I thought he was high energy and had a really strong prey drive (both of which are true) and that that accounted for why he always seemed so amped up on our walks, in the car, in the back yard, in the house... you get the idea ;-).
Understanding that he was nervous and that there were things I could do to help him relax changed our relationship dramatically. It also changed how Oliver interacted with the world and he went from being a nervous nelly who reacted (seriously over reacted) to every day stimuli to being a pretty calm, relaxed and tolerant dude. Very specifically, this meant that when we went on walks he didn't bark, lunge, pull, and spin at the site of another dog.
I learned to teach Oliver to relax. He knew the Down command as well as Sit, Come, Stand, and Fetch but what he didn't know was how to relax. The more we practiced him being in a calm, relaxed state of mind the more easily he was able to go back to that state even with distractions that would previously have gotten him excited -- inappropriately -- like seeing another dog being walked down the street. Teaching your dog how to be calm is in my opinion the single most important foundation from which to train your dog.