What is the definition of the fall line?

Stevek433 is right on. An old instructor's trick is to stand at the top of a slope that is dual-cambered- in other words, it slopes down and also tilts to one side or the other- then tell you to visualize pouring a bucket of water down the hill and tracing it's path. The way the water flows is the fall line. This is a great visualization because you have to adjust to 2 angles when skiing that slope instead of one. When a trail is also tilted to one side as you go down it, it forces you to adjust your turns (the turn on one side will need to be a bit quicker than the other) or you will follow the fall line right into the trees. Being able to read or feel the trail for the direction of the fall line is a key to understanding how to become more advanced in your skiing. Knowing the fall line allows you to let gravity work with you rather than against you.