The 'V' comes from the french 'voler' - to fly. So all aircraft carriers are CV..., which means Aviation Cruiser, with a 'N' for nuclear - don't get me started on the correct pronunciation
.
So, fixed wing squadrons inherited the 'V' and the second letter indicates Fighter (VF), Attack (VA) Fighter/Attack (VFA), Patrol (VP); except for marine squadrons which are always 'V
Mx...'. Helicopter squadrons start with a 'H' and lighter-than-air (blimps) used to start with 'Z'.
Since I'm not allowed to post links
, have a look at the wikipedia articles on USN hull classification codes and the list of USN flying squadrons.
Hope this answers the question