Indian Army

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.

Indian Navy

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.

Indian Air Force

The Air Force salutes with their palms at 45 degrees to the ground showing progress towards the skies. Earlier it used to be like the Army's salute with the palm facing up.