Understanding how to self-arrest is a necessity to travel in snow covered mountains. Without it, simply losing your footing on a slope can mean serious injury or worse. With it, a short slide down a glacier can easily be remedied and stopped (not that you ever want to lose your footing when on a glacier). These guys were descending Mt. Ritter in California (13,149 feet), traveling through the southeast glacier when one of the men lost his footing. He was able to self-arrest just fine and his crew was there to guide him and help him out.
If you need to self-arrest with an ice axe and with crampons, as this individual appears to be doing, you should get on your stomach and bend your knees so the crampons do not come in contact with the snow. The ice axe is held diagonally across the body, and the pick is dug into the snow. The ice axe acts as the brake, the crampons should be kept off the snow the whole time. More information on self-arresting can be found here.