The basic starting stance for skiing is called the V-shape or snow plow. This involves a fairly controlled movement that also enables relatively quick stop times. The V is necessary to help beginners develop their "snow legs" if you will and also helps them better understand the movements and the physical demands of the sport.
But once the V wears off in its ability to invoke a sense of fun, it's perhaps time to move on to some more challenging stances. The parallel form of moving on skis is the desired form for those who want to look like they know what they're doing. The style has the skis side-by-side rather than put into the pizza-shaped V. It looks more professional and quite frankly being able to move in this manner should be viewed with a sense of accomplishment.
Doing a parallel run the first time can be awkward, very awkward. In this movement the skis do allow for some great control and a tighter circle for turns, but it can be disconcerting at first.
Those who have mastered the snow plow are ready to move up to this level, however. Remember though that parallel does in fact equal faster. To learn it, start out with the basic V and just gradually tighten the back opening. Eventually, the V will be no more and you'll be skiing parallel.
Take your time, learn the feel and practice, practice, practice. It doesn't hurt to move to a slightly easier hill than you may be used to at this point either. The trick is learning to balance while sliding downhill at a faster rate then you're used to.
Moving up in ski styles can take a beginner a matter of a few hours, months or more. You should be the judge of when you're ready and when you are, remember it may take a little time to get used to the feel. When properly learned, the parallel is a fun, fast and more visually pleasing way to make it down a hill. Taking time, learning it right and developing the proper balance and technique, however, can mean the difference between some great runs or some disasters.