Plant That Pole
In the past, the idea was to keep the upper body quiet so the lower body could work back and forth beneath a stable torso. A strong pole plant, made during the down motion, stabilized the chest and shoulders and triggered up movement (1). Timing was everything. The pole would swing forward throughout the turn (2-3) and make contact with the snow just as the skier set his edges to stop any skidding (3). A hard pole plant combined with a decisive edge-set created very controlled but sometimes jerky descents (4). That said, this old method is still valuable in steep, tight spots.
Touch That Pole
While it's still a good idea to keep the hands out front and ready (A), the pole is now more of a feeler or antenna than a crutch. It still swings freely (B) and might (or might not) touch the snow at some time during each turn (C). It's there to set rhythm more than as a balance point. For example, the best racers in the world often don't touch the snow with their poles at all, especially in giant slalom (D). Modern freeskiers make lots of pole touches, but not always at the precise bottom of a shortening movement. Sometimes they touch while they're extending.