The army's salute is conducted with the palms open, facing the person being saluted to show that they are not carrying any weapons and that they can trust them.
The Air Force salutes with their palms at 45 degrees to the ground showing progress towards the skies
In the olden days, since the sailors were always working on their ships, their hands would get greasy and dirty. So they started saluting with their palms facing down, so as to not disrespect their seniors.
