A metastable phase is a local but nonglobal minimum of the thermodynamic potential. A finite nucleation barrier can delay conversion to the globally stable phase until fluctuations create a sufficiently large nucleus or the metastable minimum reaches a spinodal point.
Superheating is the metastable persistence of a low-temperature phase above its equilibrium transition temperature.
Supercooling is the metastable persistence of a high-temperature phase below its equilibrium transition temperature.