Supercooling is the process of chilling a liquid below its melting point, without it becoming solid.
A liquid below its melting point will crystallize in the presence of a seed crystal or nucleus around which a crystal structure can form. However, lacking any such nucleus, the liquid phase can be maintained all the way down to the temperature at which dynamic arrest occurs, and the liquid solidifies into an amorphous--that is, noncrystalline--solid.
Water has a melting point of 0°C; its dynamic arrest point is -39°C.
See also superheating.