What they're telling you to do is to use a different ball of yarn for the part of the sweater that goes up to your shoulder on the left than you do for the right.
that way you can have both shoulder pieces on your needles at one time, do a row on one side of the neck opening, drop that yarn pick up yarn from the other ball, do a row on the other side of the neck, turn your work and do it again. This way both pieces on either side of the neck will be the same length (have the same number of rows). And you use the two balls of yarn so you can do this.
Does that make sense?