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.
It is incredibly uncommon to see someone perform a max effort squat, deadlift or clean without the assistance of a weightlifting belt. I bet most of you can count the number of times you have witnessed this feat on one hand. For those that have seen this, have ever asked them why they choose not to wear a belt?
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.