The body is complex and is designed to handle variety of movements. Yoga demands many if not all the joints and muscles in the body to work at optimal levels during all the asanas. This activity is referred to as "engaging in the pose", by using all the muscles in the body to support the pose. By activating tension in the muscles simultaneously, the fascia (sheath) that envelopes the muscles create lift, improve alignment and strengthen the posture.
Beginners often rely on shifting the weight to the wrists, shoulders, low back, or neck when fatigue sets in, these sites are all vulnerable to injury. These weak areas in the body can be seen as dump sites. For instance by collapsing the joints as in rolling the wrists externally while in Downward Dog, the weight above that site compresses and compounds the weight on the joint. This in time can easily injure the tendons and ligaments around the joint.
Poses like Upward Dog or Backbends require the practitioner to tighten the gluteals in order to lengthen the spine and prevent compression of the discs. Downward Dog requires the weight to be centered in the palms behind the thumbs and index fingers while the shoulders are externally rotated away from the spine. All this happens while the quadraceps are activated and knees are internally rotated. Without this activation around the body the weight falls (dumps), diectly on the shoulders and the wrists.
For beginning and advanced yoga practitioners, doing the pose while 100% activated will help minimize injury and build stamina. So remember when the instructor says "No Dumping" tighten up the core sheath, extend, and engage fully in the pose.