Supercooling is cooling water below the freezing point such that is still a liquid. Ice crystals grow at the freezing point and below, but the "beginning of a crystal" (a crystal nucleus) must be present, typically some (possibly very slight) impurity, e.g., water with minerals dissolved. Pure water spontaneously forms crystal nuclei (crystal nucleation) of its own water molecules at a somewhat lower temperature, at which point freezing of the pure water occurs spontaneously. Supercooled water (i.e., water in the supercooled state) between these temperatures is somewhat stable, and can also be present during the time that crystals are growing.
This "supercool" terminology is sometimes used (in analogy) for phase transitions other than water freezing, including those at the subatomic level, such as in the very early universe.