In the most extreme case consider where you enter a wide but short run at the top from one side of it instead of from the middle, and the run ends at a chair in the middle.
If you take a high line to the centre of the run and then go pretty much straight down it then you will ride down the fall line and spend generally equal time on both edges. If you ride in a mostly straight line from the entrance to the fall line you are crossing the fall line and you arent riding the fall line but more across it so you will spend most of your time on one edge, which in extreme cases is kind of boring, sometimes its more fun to get to the middle of the run rather than just getting pushed to the centre as you go down one side.
A friend of mine pointed out to me that Whistler Mountain's runs are more often cut across the fall line as opposed to Blackcomb. I'd never thought about this but I did notice it next day, and I did prefer to ride some runs on blackcomb where I could ride the fall line intead of having to mostly go across it.
It's certainly worth looking ahead at the shape of the hill to see where the fall line changes to choose your route.
As far as above/below the fall line I'm not sure about this, other that that when carving your normally switch edges as your board's nose crosses the fall line, ie. when it's pointing down at the max angle of the hill. If you switch edges early you are I guess turning above the fall line, and then you carve across it.