I think it's the oldest magical item recorded. In the Odyssey, of course, Circe uses a wand when turning Odysseus's men to swine. Something that old probably had deep metaphorical significance, because the best magical items are metaphors for the magic they do. Wands are awfully general purpose in stories. . . .
Of course, they are really sticks, and sticks are real old tools. Chimpanzees have been known to flourish them to look more threatening -- and that's certainly one aspect of them -- a wizard waves a wand as an extension of his hand to look more impressive, so that we get more impressive results. It is amplify gestures.
And there's Circe's usage, which is basically that of a finger -- to point. One points at what one wishes to enchant.
Hmmm -- of course, we also use sticks to put a safe distance between us and poking things to move them. I don't know of any magical uses of wands to emulate that. Still, amplifying gestures and pointing at things are such fundamental things in magic that it would be an obvious usage.