The term supersaturation refers to a solution that contains more of the dissolved material than could be dissolved by the solvent under normal circumstances. It can also refer to a vapor of a compound that has a higher (partial) pressure than the vapor pressure of that compound.
Small particles (seeds) can trigger the separation of the dissolved material from the solvent or condensation of the vapor. Seeds triggering the condensation of vapor are referred to as condensation nuclei, as in the case of water vapor. In the solid form these seeds can lead to the formation of crystallites or even large single crystals. Supersaturation is a measure of the deviation of a dissolved salt crystal from its equilibrium value.
Carbonated water is a supersaturated solution of carbon dioxide gas in water. At the elevated pressure in the bottle, carbon dioxide can dissolve in water more than at atmospheric pressure. At atmospheric pressure, the carbon dioxide gas escapes very slowly from the supersaturated liquid. This process may be accelerated by the presence of nucleation sites within the solution, such as small bubbles, caused by shaking the bottle, or another solute, such as sugar powder or a widget. A Diet Coke and Mentos eruption is a rather extreme example. Some beverage products such as ales and stouts e.g. Guinness rely on this effect to produce the 'head' on the surface of the poured product. This has led to the invention of the widget, a device developed to produce enhanced bubble seeding in liquids, especially with dual supersaturated gas phases (carbon dioxide and nitrogen) (see patents by Fitzpatrick and Kuzniarski).
Supersaturated solutions of sugar and water are commonly used to make Rock candy.