Thanks to the Harry Potter series, and other works of more modern fantasy like the Dresden Files wizards have become cool again. Once relegated to the pages of dime novel fantasy and Dungeons and Dragons role playing books wizards have shaved off their beards, hit the gym, and become powerful protectors of humanity in modern fiction. The re-imagining has led a lot of fans to question why wizards were always learned old gray beards with a penchant for philosophy, though. Fortunately there's a simple answer to this question.
That image is exactly what the term originally referred to.
The Origin of The Wizard
The word wizard entered general use in the 14th or 15th century, which means that it came out after the Black Death and right around the time of the witch craze.
The word is actually two different words put together; wys meaning wise, and ard (yes ard is a word). The result is a word that means "one who is wise," or "one who excels at wisdom." The term was originally meant to refer to philosophers, scholars, and other learned individuals, but during the Middle Ages the line between philosophy and magic blurred considerably. The result was that in addition to being learned in science and philosophy wizards were supposedly able to see the future, and to possess the ability to work all kinds of spells.
Then in 1922 wizard became a British slang term for anyone who was supernaturally gifted at something. Pinball, computers, darts; the activity didn't matter. The point was that the person with skill was a "wiz" at it.
Is That All?
Yep, that's pretty much it.
We've had dozens of terms for magic users and spellcasters throughout history. In the European north there were warlocks, and in the Middle East there were sorcerers. There were witches in the west, and they eventually got mixed up with mages, occultists, Wiccans, pagans, neo-pagans, and the list goes on and on. The point is that every word has its own, unique history and that if you dig deeply enough you'll be able to find it. Sometimes you won't find anything interesting, but other times you'll find that a word that means one thing today meant something very, very different in the near or distant past.