An induction recording is a recording made with a small device available at Radio Shack called a "Telephone Pickup". It's basically a small suction cup with a wire and audio output on it. When the suction cup end is put on a speaker (either on your phone headset, or at a Disney Theme Park), the device inside picks up on the magnetic signal, and sends it through the wire, and hopefully into the recording device you've plugged in at the other end (digital recording devices like Minidisc players seem to work best). This is an overly simple explanation and doesn't include all the tips and nuance that it takes to get a really good recording. Several on this board could really explain better how to do it. It can produce results that range from absolutely phenomenal to pretty poor. But anyway, anytime you see something labeled induction, that's basically what it means.
I tried it for the first time at DLRP this summer and got what (to me) were really good results (minidisc recorder).
It does seem like magic but it works and the basics are just as X-S Tech says. The secret is learning where to place the pickup (a small distance of less than half an inch can mean a BIG difference in quality).
Think of the pickup like a directional microphone (it isn't but the idea works well).
It's advisable to have headphones to hear the sound being picked up as well- rather than relying on an automatic level etc.
The worst bit is sitting around while you record and listening to the family complain that they want to go on a ride
Do try it, it's great fun and something rather "special" to bring home as a memory.