To carve a turn, you must put the ski on edge, bend the ski in an arc and press the downhill (outside) ski into the snow. A low body position is important to accomplish this.
In getting into this position, your body must fold, somewhat like an accordian, so your weight will be distributed over the center of your skis. Drive your knees forward so your shins push against the front of your boots, drop your hips to compensate for your knees going forward and lean forward slightly with your upper body to balance your hips dropping back (see photo).
A low body position is important for two reasons: angulation and pressure. When one skis in an upright position, driving the knees into the hill (angulating) is nearly impossible. The knees cannot move laterally when the legs are straight. You must bend your legs and drop into a low position to drive your outside knee to the inside of the turn. The more you push your knee laterally, the more you will put the ski on edge.
As far as pressure is concerned, your limbs are strongest when they are bent. Try to push against the floor as hard as you can when you're standing straight. You can't apply very much pressure. Then drop into a low body position so your legs are bent. You are much stronger and can exert more pressure. The more pressure you apply, the more the ski will bend.
Most skiers don't get low enough. Drive your knees forward to about a 45-degree angle from the skis, balancing your weight between the balls of your feet and the front of your heels. Loosen or undo the top buckle of your boots if you feel they are preventing you from driving your knees to a 45-degree angle.