Alignment and Action: holding heaven and earth in the heart
Adho Mukha Svanasana, otherwise known as Downward Facing Dog pose is an intermediate level arm balancing pose and inversion. It is a primary pose in most vinyasa (flow) style practices. Correct alignment of the hand, wrist and shoulder joints, along with a balance of strength and flexibility in all of the major muscle groups in the upper and lower body as well as activated core musculature is all needed in this pose to find the sweet spot at the center of the heart.
The physical practice of yoga strengthens the human vessel, the heart-body-mind, so that we can withstand the pressure of growing a strong spiritual life and presence in the world. Downward Facing Dog pose exemplifies this idea. The requirements of this pose include strength, balance, alignment and endurance. The same qualities that are required to live a life of love and compassion, yet to be strong and grounded enough to do ones part in the creation of a more beautiful world the heart knows is possible.
Downward facing dog creates space in the body by lengthening the spine. It also strengthens the wrist and ankle joints and energizes the physical, mental and emotional body. Pressing our hands and or feet towards the earth allows us to become grounded emotionally and physically. The hands are part of Anahata, the heart chakra and the feet are governed by Muladhara, the root chakra. As this is considered an inversion, it also helps to energize the body and mind and connect with the higher chakras, particularly Ajna (third eye chakra) and Sahasrara (crown chakra).
For all you anatomy geeks out there, Ray Long MD illustrates the some of the muscles involved in this pose with an explanation of how to focus awareness for the greatest benefit.
The illustration below is provided by Leslie Kaminoff, an expert in yoga and breath anatomy. The illustration below, from his book Yoga Anatomy, allows us to view the pose from both anterior and posterior angles. Please note three important muscles in the illustration.
The latissimus dorsi which can be seen in detail below is an accessory breathing muscle; it expands the circumference of the rib cage with inhalation. Slow, even, complete breathing promotes endurance and efficient muscle action. The serratus anterior acts to pull the scapula forward around the thorax. Also of importance in this pose is the triceps brachii which extends the forearm at the elbow joint and adducts the arm at the shoulder joint. In this pose the long head of the triceps is working in an eccentric contraction. I cannot overstate the importance of strengthening weak triceps.
And now just a little more about the latissimus dorsi. The muscle originates from the sacrum and spinous processes and supraspinous ligaments of all lower thoracic, lumbar and sacral vertebrae, lumbar fascia, posterior third iliac crest, last four ribs (interdigitating with external oblique abdominis) and inferior angle of scapula.
The latissimus dorsi forms two-thirds of the superficial back muscles, originating from the posterior iliac crest, sacrum and thoracolumbar fascia, rotating 180 degrees before inserting on the inside of the proximal humerus. This "twist" increases the torque generated by contraction of the latissimus dorsi. This muscle draws the arm down and toward the body from the overhead position, internally rotating the humerus. Tightness of this muscle limits the ability to extend the arms overhead. (Ray Long)
BKS Iyengar in Light on Yoga provides a detailed description of the effects of Adho Mukha Svanasana:
When one is exhausted, a longer stay in this pose removes fatigue and brings back the lost energy. The pose is especially good for runners who get tired after a hard race. Sprinters will develop speed and lightness in the legs. The pose relieves pain and stiffness in the heels and helps to soften calcaneal spurs. It strengthens the ankles and makes the legs shapely. The practice of this asana helps to eradicate stiffness in the region of the shoulder-blades, and arthritis of the shoulder joints is relieved. The abdominal muscles are drawn towards the spine and strengthened. As the diaphragm is lifted to the chest cavity the rate of the heart beat is slowed down. As the trunk is lowered in this asana it is fully stretched and healthy blood is brought to this region without any strain on the heart. It rejuvenates the brain cells and invigorates the brain b relieve fatigue. This is an exhilarating pose. 
In his Yoga Resource Practice Manual Darren Rhodes provides succinct instructions on how to find this pose.
(from bharmanasana AKA table pose):
Move the knees back four to six inches and curl the toes under
Live the knees and straighten the legs. Push the hands down and forward, and stretch the hips up and back.
Relax the neck and gaze straight back. Hold the pose and breathe.
To come out, bend the knees and place them on the floor. Bring the shoulders over the wrists and walk the knees forward until they are directly below the hips.