Think of your chest as a balloon pump or bicycle pump. When you expand your diaphragm and chest muscles, they draw air into your lungs, just as a pump draws in air when you pull back the handle. When you contract the muscles of your chest wall and diaphragm, they squeeze air out of your lungs.
Emphysema overstretches your lungs so much that they can't contract. Try as you may, you can't squeeze the air out of them. It is as if someone stuck something under your rib cage and diaphragm to keep them stuck in an expanded position, much like someone putting a stop between a door and jamb so the door won't close. The rib cage and diaphragm can't push out the air in your lungs, and they can't expand much more to draw in new air.
In screening patients for lung-volume reduction, surgeons look for people whose emphysema is unevenly concentrated in small parts of their lungs, which are otherwise composed of relatively healthy tissue. Then they can cut out the useless parts of the lung that are propping open the diaphragm and chest, leaving enough healthier parts for the patient to get enough air to live on.
The operation itself takes only about an hour, and with the technique Dr. Joel Cooper of Barnes-Jewish Hospital uses, most of that time is spent carefully sewing the rib cage and chest muscles back in place to minimize scarring.