when punching not properly - your punch might be feel more like your pushing with your hand which is far less powerful and damaging...
I think by SNAP your instructor means you should kind of throw (not push) your fist forward - try to relax your arm, do not try to control or limit it's reach - you just need to get a feel of it, then when you know what you are looking for it will be easy to control it.
Hard to explain - has to be shown. Ask instructor to show you how it should look and feel like.
HONESTA MORS TURPI VITA POTIOR