The high hang snatch can be used for a number of different reasons, however it is most commonly used to teach beginners how to properly pull underneath the barbell. The decreased pulling distance makes the lift much more simple than when snatching from the floor.
The first pull is arguably the most important phase of the snatch and the clean. Your starting position, and how you pull the weight from the floor determines the trajectory of the barbell. Even the smallest error during this first movement can easily result in a missed lift.