That's a tough one, even the readers of this group have argued over what defines backcountry skiing. However, a reasonable definition may be that backcountry skiing is the sport (and art) of skiing in places and terrain that have not been altered by people, and away from snow that has been groomed for skiing.
While many people would argue about what defines backcountry skiing, not many would have trouble answering a better question.
Why do people backcountry ski? Simply because its fun.
Backcountry skiing is one of the most relaxing, pleasant and rewarding activities of our lives. We enjoy the terrain we travel through, and we enjoy the solitude that a little effort will bring. We enjoy the company of our companions, and we find the skiing to be unmatched in quality. What more could a skier ask for?