Most solutes have some degree of solubility in aqueous solution, which is the typical solvent. The solubility is typically a function of temperature in that a hot solution can solvate more solute than a cold one.
A #"saturated solution"# is described when there is an equilibrium between dissolved and undissolved solute. We can take such a saturated solution with EXCESS UNDISSOLVED SOLUTE, heat it up, and bring all the solute into solution. When we cool this solution down, sometimes we can get a cold solution WITHOUT any solute precipitating. Such a solution is #"supersaturated"# with respect to the solute because it contains greater than an equilibrium quantity of solute.
A #"supersaturated solution"# is a metastable phenomenon because we could add a seed crystal or scratch the side of the container to crystallize out the solute, and restore saturation, that is restore a solution whose concentration is the same that it would be if the solute were in equilibrium with undissolved solute.
These ideas are very poorly appreciated at A level, so it would be a good idea to test your understanding of the principle.
