The hand salute is such a routine tradition in the military that you may never wonder where it came from.  One tradition dates back to the days when knights would lift their visors to identify themselves to superiors as they passed.

A tradition dating back to early records of military courtesies holds that men-at-arms crossing each other’s path would raise their right hand to show they were unarmed.  The junior would raise first.

But probably the predecessor of the modern salute is the custom of  juniors removing their headgear in the presence of superiors.  In the British army, the custom became a simple grasp of the visor.

The British soldiers’ salute with palm out is distinct from the American palm-down salute.  The folklore says the palm-down signifies having lost a war.  But more likely, Americans adopted the British navy’s salute: sailors saluted officers with palm down because it was undignified to show a dirty hand to an officer.