Normally when water cools down, the molecules get all chummy and lock together. The longer the cooling down takes, the bigger the crystals they can make before there's not any free water molecules left.
If the temperature drop happens quickly, the water molecule doesn't have time to form big crystals. You end up with a hodgepodge of small crystals.
Here, the magnets keep the water molecules moving around, which prevents crystal formation. It has to do with the fact that water molecules have polarity due to their charge. Moving the magnetic field around moves the molecules. When you turn off the magnetic field, it's like all the water molecules realize at the same time that "oh shit I need to be ice right now" and make crystals as fast as they can. That way, you end up with a gigantic collection of absolutely tiny crystals.
You can do something similar with unopened bottles of water. If you put a pack of them in the freezer or outside overnight in freezing temperatures, if the water is pure enough it will still be liquid. Any sudden jolt will then cause rapid crystallization (although with water bottles it will still be a slurry). video here http://www.youtube.com/watch?v=fSPzMva9_CE