The push between the legs basketball dribble drill is going to help you practice being able to back dribble out of a potentially dangerous situation with the ball. One of the best ways to prevent turning the basketball over, is to keep yourself out of places on the floor where you can be trapped or where there is a lot of congestion. As a ball handler, if you can recognize those situations quickly and then avoid them, you will save yourself a lot of trouble. This basketball drill is designed to give you a way to get out of high potential turnover areas.
A great example of this would be coming off a ball screen where the post defender is hard hedging or trapping. You don't want to dribble right into the post defender. Instead you want to use the screen and then push dribble out so they have to extend farther out, then you can get the angle on them and drive the ball, or pass to an open teammate.