Backcountry extreme skiing or snowboarding is exploring ungroomed and unmarked terrain either just outside ski area boundaries or in remote areas. In Europe, this is often called “off-piste” skiing. This is definitely one version of "extreme" skiing and riding.
Backcountry skiing and snowboarding on ungroomed and unmarked terrain should only be done by experienced skiers and riders who understand the dangers of avalanches and have appropriate equipment to deal with snow slides and unexpected emergencies. Other potential dangers include exhaustion, getting caught in unexpected blizzards and losing one's way.
It is definitely a stupid, potentially dangerous move–and in some cases illegal–to duck under roped-off or closed gates on ski-area boundaries that lead to backcountry skiing. (You may be charged for the cost of rescue if you get lost, hurt or caught in an avalanche – and survive.) You should never duck under a rope barring people from entering inbounds extreme terrain. Ski Patrol may have the slope closed because the snow is unstable and avalanche control work may be required.
Several western resorts offer inbounds backcountry-style experiences, similar to out-of-bounds extreme skiing for expert skiers and riders. Some resorts, such as Jackson Hole and Aspen, have specific clinics for people who want to learn how to ski or ride in the back country, plus backcountry guide services.