I think she means that if you start at one end and knith the whole thing you'll get those nice points at the ends of the rows (where the beads are attached) on one end of the scarf, but as you get to the other end and bind off, it will be concave like the red line in the picture shows. So one end will have sticky-outy bits while the other will have sunken in bits and no points to hand beads from. It would look kinda lopsided.
So to make sure the ends look the same when they're hanging down, she cast on once, knit one ball (of the two) and then put the live stitches on a stitch holder and then set the whole first piece aside. Then she cast on again (to make the other end that hangs down identical to the first cast on edge) and continued to knit almost to the end of the second ball. Once she had nearly finished the second piece, she grafted the two pieces together at the live stitch ends (ie: she took the live stitches from the first piece off the stitch marker and put them back on a needle then joined the two "live" ends by using a three-needle bind off technique - which is easy to do). So the two ends are essentially knit so that they meet in the middle (behind the neck) where they're grafted together and they look the same when hanging down.
This is all done because the stitch has a certain direction to it.
I hope that helps clarify things... I think you could easily do this scarf!