The Steve Nash between the legs partner passing drill is going to be both a ball handling and passing drill. What it is going to work on is the ability to make a push pass off of a dribble. This is important for ball handlers because you never know when a teammate is going to come open off a screen or cut, and you may not have the chance to gather the ball with both hands before making the pass.
The reason this basketball drill is named after Steve Nash is because he really mastered this type of pass, and was constantly using it throughout the course of a game. In his prime Nash was one of the best passers of all time. However, this pass is a little bit more advanced. So before using this type of pass in a game, make sure that you have really mastered it. You don't want to be inaccurate with the pass or float it, because this will most likely end up in a fast break basket for the other team.