The "parallel" in the gun's name refers to the comb of the stock, which is parallel to, (or nearly so) the barrel. A normal stock drops toward the butt. The advantage of such a stock is that head placement is less critical than with a normal stock, where moving your head fore or aft will give you a different angle of view over the barrel. The stock is therefore recommended for sporting clays, where a consistent mount at a variety of target presentations is required. Some hunters also extoll the virtues of a parallel stock, for the same reason.
Be aware that the 391 Parallel has a little more drop at comb than a standard Beretta stock with the shim for the most drop installed. I think that Beretta still built some cast into the stock, which will not do you any good as a southpaw. The best bet is to try the gun and see. Some people like the parallel stock, others do not. If it does not fit you, all the theory in the world won't help.
Sharptail