According to British military traditions, the reason that
the British salute with their palms facing toward the
person they're saluting at is because a soldier had killed
a superior officer by being able to hide a pistol in the
palm of his hand. This then forced the British military
to change their saluting process and had them salute as
above and being able to see what's in their hand.

Submitter comment: I learned this from my uncle while we were on vacation
in England.

Where learned: ENGLAND ; WINDSOR