On a ball screen the defense can choose to guard it several different ways; switch, show, go under, trap, etc. For this ball screen retreat dribble situation the drill is going to work on if the defense traps or blitz's the ball screen. Instead of just picking the ball up when you get trapped and playing into the defenses hands, you want to be able to make them pay for trapping you on the ball screen. The ball screen retreat dribble attack drill will help you work on navigating a ball screen trap and then making the defense pay for trying to trap you.
A lot of times when a defense traps the ball screen they are going to have the back side defenders rotate and try to steal the pass out of the double team. Being able to retreat dribble and read the floor out of a ball screen trap is a great tool to have. Also it allows you to keep your dribble alive and then attack the big mans outside foot with space, and if you are able to get past the trap your team will be able to have numbers attacking the basket. This type of move is one of the basketball fundamentals of using a ball screen.