Originally Posted by therusty
One way to get a feel for the "forward hip movement" is to stand on tip toe with one foot but move your hip foreward as you raise your heel. You'll notice that the hip movement is both forward and diagonally to the side of the still flat foot. If you do this while you let your other leg collapse, the feeling will be even more pronounced.
While I generally agree with what therusty has said, I would caution you to recognize that this is a drill or exercise to get you to emphasize moving the hips forward and diagonally. Pressing on your toes or attempting to stand on tip-toe while in ski boots, however, can actually cause you to move back and lose the gentle shin contact you want with the front of your boots.
The idea of extending into the new turn is valid (standing on tip-toe is an extension move), but you don't want it to push you into the back seat.
Something that might also help with moving the knees and hips forward into the new turn, as well as lightening/tipping the new inside (old outside) ski is actually attempting to pick up the big toe of the new inside foot as you transition into the new turn. This increases ankle flex, pulls the shin forward against the front of the boot, and tips the foot toward the little toe edge, in the direction of the new turn. It's important to allow this movement to pull your knees and hips forward, rather than sitting back and picking up the front of the ski! Remember what Pierre said about getting your femurs a bit more vertical. This will help keep your hips over your feet, rather than behind them.
Lightening/tipping the new inside ski is often a flexion move which can complement the extension of the new outside leg. It's good to have both available, and you may find yourself using a blend of both, depending on the circumstances and the intent.