This ranks as one of those "who'd a thunk?" late arrivals to the English language. Not in every sense, of course, but I think you'll be surprised by some of the years on this!
Okay, so "show" as in act or performance is as old as you might expect, coming from the 1300s. And an appearance put on to deceive, or an ostentatious display are from the 1500s. As a verb, it's even older, though with a twist unique to English. Ours evolved into a meaning of "to make known" in the 1200s, but the correlating word in other languages still carried its original meaning of "to look at."
But some of the meanings we use most often are the ones that'll get you.
Did you know, for instance, that "show up" didn't come along until 1888? That's after "show biz" which is from the 1850s! And it's even after "I'll show you!" That particular meaning comes from the 1820s.
Interesting, huh? =)
Hope everyone has a great Monday!