http://www.qmmuseum.lee.army.mil/history/vignettes/respect1.html ORIGIN OF THE HAND SALUTE No one knows the precise origin of today’s hand salute. From earliest times and in many distant armies throughout history, the right hand (or "weapon hand") has been raised as a greeting of friendship. The idea may have been to show that you weren't ready to use a rock or other weapon. Courtesy required that the inferior make the gesture first. Certainly there is some connection between this old gesture and our present salute. One romantic legend has it that today’s military salute descended from the medieval knight's gesture of raising his visor to reveal his identity as a courtesy on the approach of a superior. Another even more fantastic version is that it symbolizes a knight's shielding his eyes from the dazzling beauty of some high-born lady sitting in the bleachers of the tournament. The military salute has in fact had many different forms over the centuries. At one time it was rendered with both hands! In old prints one may see left-handed salutes. In some instances the salute was rendered by lowering the saber with one hand and touching the cap visor with the other. The following explanation of the origin of the hand salute is perhaps closest to the truth: It was a long-established military custom for juniors to remove their headgear in the presence of superiors. In the British Army as late as the American Revolution a soldier saluted bv removing his hat. But with the advent of more cumbersome headgear in the 18th and 19th centuries, the act of removing one’s hat was gradually converted into the simpler gesture of grasping the visor, and issuing a courteous salutation. From there it finally became conventionalized into something resembling our modern hand salute. As early as 1745 (more than two-and-a-half centuries ago) a British order book states that: "The men are ordered not to pull off their hats when they pass an officer, or to speak to them, but only to clap up their hands to their hats and bow as they pass." Whatever the actual origin of today’s hand salute, clearly in the tradition of the US Army it has always been used to indicate a sign of RESPECT – further recognition that in the profession of arms military courtesy is both a right and a responsibility of every soldier. Compiled by the U.S. Army Quartermaster Corps Historian Fort Lee, Virginia

Raising or removing headgear before a leader makes the most sense, but I don't think the origin is known.

it originated during the Middle Ages when Knights would meet on a road. Since they wore metal visors over their faces, baring the face by lifting the visor was a way of signalling that they intended no harm. When armor became obsoltete because of gunpowder, the custom of rasing the hand to the upper face continued as a way of honoring other soldiers. It was only recently that the US military forbade use of the salute between people of the same rank, or between any two enlisted men.