I like to think of skiing as an entire domain. In broadest terms, the objective when skiing is to make it to the bottom of the hill in one piece, injury-free. If you don't make it to the bottom, you can't drive yourself home! (unless you're skiing into a valley, in which case you may need to make it to the top of the hill again.)
When you start looking at the sport disciplines within skiing, more goals present themselves. Goals are still open and unique to each individual, but often include:
slalom/gs/dh/superG: race the gates in the fastest time.
freestyle: create the most unique combination of manouvers among all competitors.
ballet: avoid breaking your legs.
off-piste: manage all terrain conditions at all pitches with consistent speed.
carving: create perfect railroad tracks on increasing terrain complexity.
touring: achieve a great cardio workout, ski an untracked run.
long-term skiers: achieve a lower-impact skiing style conducive to many decades of successful skiing
Last but not least, as I believe BB once said, skiing is a sensation-seeking sport. A big part of the objective of skiing for most skiers above the intermediate plateau is to recreate (or find!) those amazing sensations of alternating weightlessness and compression, rotation and counter-rotation, fast feet, and constant motion downhill. The goal of instructors is to enable our learners to achieve whatever objectives they've set out for themselves--or give our learners a taste for those different sensations.