Lateral balance is your balance from side to side. In skiing, you must lean to the outside of a turn rather than to the inside, as you normally would do when riding a bike or motorcycle or driving a car. The reason for this is that you must weight your downhill -- or outside -- ski for stability.
Even though your skis may be only six inches apart as they travel across the snow the terrain will be different for each one. If both skis are weighted, the difference in terrain will cause one to dig in while the other slides. However, if only one is weighted, that ski will track through the snow following the terrain.
Theoretically, you could weight either ski. As long as all your weight was on one ski, that ski would track through the snow. You would be stable.
However, because the inside of the ankle is stronger than the outside, you will have more stability if you weight the downhill ski. (Just as in tennis, the inside of the wrist is more powerful than the outside. Most people have a stronger forehand than backhand.)
Many skiers would swear they ski with all their weight on their downhill ski. Usually they've distributed their weight over both skis. The one way to be sure is to concentrate on getting all your weight off your uphill ski. Your inside ski may be riding along the snow, but there should be no weight on it (See photo).
Next: lateral movements.