Definition
Supercooling is when a liquid gets colder than its freezing point but stays liquid anyway. It is fully ready to turn into ice and is just waiting for a trigger, so even a tiny bump or one speck of dust can make ice spread through it in an instant. Freezing releases heat, which pushes water's temperature back up to about 0°C (32°F), so usually only part of it freezes and you get slush.
The magic trick of a bottle that turns to slush
Slide a bottle of water into a freezer that's cold enough to freeze everything solid, then carefully take it out. It looks like plain cold water, still sloshing around. But the moment you tap the bottom or twist off the cap, the whole clear bottle turns white, like magic, and becomes icy slush.
Water normally starts to freeze at 0°C (32°F). But for water molecules to line up neatly into an ice crystal, they first need a center point called a crystal nucleus, something for the molecules to cluster around and copy.
If the water in the bottle is very clean and has been sitting perfectly still, its molecules can't find a place to start. They just hang there, waiting. Then you tap the bottle. Tiny bubbles and a small shock appear, and that's the signal. Ice races out in every direction in an instant.
A bit more precisely: why doesn't water freeze below 0°C?
To be more precise, water molecules have to get over an energy hurdle before an ice crystal can start. A tiny bit of ice made from just a few molecules is unstable because of the pull of its own surface, so it easily breaks apart and goes back to being water.
Only when this little ice seed grows past a certain size can it pull in the water molecules around it and grow into big ice. Tiny specks of dust floating in the water, or rough scratches on the inside of the container, give these seeds a solid place to settle.
Extremely pure water has no impurities and no scratches, so it has no such footholds. It can stay liquid until it drops to nearly minus 40 degrees. Physicists call this homogeneous nucleation, and it really does happen inside clouds high in the sky.
The winter road menace and the warm hand warmer
Supercooling looks like a neat magic trick, but in nature it can cause real danger. A classic example is freezing rain on winter roads. Along with melted snow or rain that refreezes, it is one of the things that can create black ice (a thin, nearly invisible layer of ice on the road). Raindrops fall through freezing air and get colder than 0°C (32°F), but they can't freeze in midair. They reach the ground still supercooled.
When these cold drops hit the asphalt and get jolted, they seem to have been waiting for it. They instantly turn into a clear, slippery, thin sheet of ice. It's hard to see, and that makes it a major cause of winter traffic accidents.
Supercooled water droplets also slam into airplane wings and freeze there when planes fly through high clouds. This is called icing. On the helpful side, the click-to-heat hand warmer is an invention that puts this very idea to good use. It keeps a liquid supercooled when it should have hardened. When you bend the little metal disc inside with a click, the shock sets off freezing, and the liquid hardens while giving off heat.
Common misconceptions
Water always turns to ice immediately once it drops below freezing (0°C).
0°C is just the temperature at which ice can start to form. Without a crystal nucleus (such as dust or a small shock) to get it going, water can stay liquid even dozens of degrees below freezing.
Where you meet it
If a water bottle sits in the freezer for just the right amount of time, tapping it can turn the whole bottle into slush within seconds. Leave it too long and it just freezes solid.
On a below-freezing day, rain can freeze the instant it hits the ground or a car windshield. This is freezing rain.
In one sentence
Water can get colder than its freezing point and stay liquid because it has no ice seed (crystal nucleus). Then one small disturbance makes it freeze almost instantly.