Perhaps the most obvious thing that everyone understands about skiing parallel is that both skis need to twist or pivot simultaneously and to the same degree. We call this a steering angle.
Secondly both skis need to tip onto a similar edge angle. If both skis are tipped the same amount against the snow surface they will bend the same amount and therefore the additional steering angle built into the ski design will allow them to travel in the same direction.
Remember, a ski that over grips is hard to steer!
Vertical Pressure Control - If one or both skis are stuck in the snow (or have too much pressure) they become difficult to twist. On the other hand, if the skis are not in contact with the snow there won’t be any steering forces.
Lateral Pressure Control - Over or under pressuring one ski in favour of the other can cause them to deviate from their path.
Fore/aft Pressure Control - Over pressuring the tip of a ski often causes it to over-steer. Over pressuring the tail of a ski often causes it to under-steer. If either of these things happens to one ski more than the other, it has a tendency to stray from parallel.
Deviations from parallel manifest in a variety of ways, each with their own specific cause…