Indeed, speculative fiction is filled with examples of technology powered by magical means. From spaceborne shipyards powered by magical energy fields to cameras that house imps who literally paint pictures on demand. The name of this entry comes partially from one of my favorite video games of all time, Final Fantasy VI, which features an antagonistic empire that forcibly extracts the magical properties of beings called Espers and applies them to mechanized suits of battle armor. They call this process Magitek, the fusion of magic and technology.
As with most tropes, if you peer back far enough into the myths and legends that inspire much of our modern fiction, you can find the early seeds of magitech. For instance, you have the Greek deity Hephaestus, who was worshiped by blacksmiths and stoneworkers as the god of fire and craftsmanship. According to Greek mythology, he crafted many of the weapons and armor of the Olympians, which were almost always imbued with magical properties of some kind. He also built magical automatons out of metal that served him in his craft, including tripods that would travel to and from Mount Olympus at his beck and call.
The wizards of the Harry Potter universe tend to frown upon the use of "muggle" technology, using a magical equivalent instead, like self-writing quills that serve as word processors. In The Chamber of Secrets, however, we see an otherwise ordinary automobile enhanced with magical properties—most notably, the ability to fly.
Thus far, my own fantasy has yet to approach the use of magitech. My fantasy world is light on magic altogether, but when it does appear it stays firmly in the realm of the other, seldomly intersecting with that of the mundane. That being said, I'd love to play around with the concept one day. As someone who adores both science fiction and fantasy, the magitech trope can be an awesome opportunity to bring both realms together in interesting ways, depending how you play it.
And I think that gets to the heart of the appeal of tropes like this one. Magitech brings the real and the unreal within the same plane, at once making the forces of the supernatural and metaphysical far more relatable. Your traditional crystal ball or magic wand is still very capable as a plot element in the hands of a skilled writer, but let's face it: that stuff can also be pretty boring. It's been done. Give me a bazooka that shoots fire elementals instead, and you have my attention.
Recommended Reading:Magic, Inc. by Robert A. Heinlein
The Discworld series by Terry Pratchett
The God Engines by John Scalzi
Final Fantasy VI
Star Wars: Knights of the Old Republic