A head-and-shoulder move in basketball is when a player fakes one way with their head and shoulders and either dribbles or shoots going the other way. In simpler terms, they lean their head in one direction, and then quickly jerk it back and go in the opposite direction. It is a misdirection type move that serves the purpose of getting by a defender.
A head and shoulders move can also be done without the ball. A player fakes with their head one way and runs the other in an attempt to get passed the ball.
A head-and-shoulder crossover in basketball is where a player fakes one way with their head and shoulders, but crosses over with the ball going the other way. Compared to a basic crossover the head and shoulder crossover just adds in the head fake. That in most cases gives it a higher rate of success.
In order for a head and shoulder move to be effective the fake really has to be sold. The headfake should be crisp and believable. Looking in the direction that you are faking can sell the defender as well as turning your body the same way.
Head and shoulder moves are used at any point during the game by an offensive player. They are very common and can be seen on just about every possession. That being said there are times when it is more effective than others.
Head and shoulder moves are the most effective in transition offense. That is because usually the offensive player is running quickly and the defender has less time to react. That way the move will force the defender into a split second decision which is a tough position to be in.