You’ll trigger this quest when you reach the 12th of Winter. You’ll get mail, as usual; pop it open to begin the request. (It’s also possible this quest only triggers when you reach the lowermost depths of the Mines. I’m not entirely possible. Anybody care to confirm this one way or another?)
The Wizard petitioner is asking you to bring him a Void Essence. Void Essences are relatively common objects… the caveat being that the creatures which drop ‘em are in the absolute depths of the Mines, from level 80 onwards. They’re regular drops by Void Spirits, which come in two varieties: big, dark, hulking creatures that have heads that look a bit like onions (depicted above), and smaller, chubby creatures wearing tribal masks. Killing either one will likely earn you a Void Essence.
Take the Void Essence to the Wizard once you have one. He lives in the Wizard’s Tower in the far southwest of Stardew Valley, a ways west of Marnie’s Ranch, and is there pretty much all day long. He’ll give you 1,000 gold for the delivery, found in the quest’s Journal entry.