I think he is telling you to slip to your right a little (for orthodox). What he is getting you to do is move your head so it isn't in one spot and thus easily hittable. It can help to evade an incoming jab, while landing your own. Alot of fighters keep their head in one spot when punching and the head is right there begging to be tagged over and over again. It's the same as leaning to your left for a right hand. It's all about moving your head out of an easy line of attack. Cotto is very good at doing this, as is Calzaghe and Hopkins. It's often to do with not being fast enough to get off your own shot thus you go defensive and offensive at the same time. It can also be due to a lack of power so the guy can punch when you are punching because he doesn't respect your punch. I advise you don't do it on every jab. Throw a text book jab at the guy and see what happens. If he is catching you then you'll want to move your head. It will best be used against a tall guy who has a longer reach than you. He'll out jab you as you come in or out, thus you need to move your head out of the line of attack from which his jab will come.
