Solubility is the amount of a substance that can be dissolved in a given amount of solvent
Solubility changes depending on temperature and pressure.
To the right are the solubility curves for different ionic slats dissolved in water. Most increase in solubility with temperature.
When the maximum amount of solute at a given temperature is dissolved into water the solution is said to be saturated. Looking at the graph above, 80g of NaNO3 can be dissolved at 10° C. If there is less than that dissolved the solution is said to be unsaturated.
Heating a solution will allow more solute to be dissolved. As the solution cools the solubility decreases, but the already dissolved solute will not precipitate (come out of the solution) instantly. Therefore there is a period of time when more solute is dissolved than the solubility allows. This solution is said to be supersaturated.
If you have ever made rock candy, then you have made a supersaturated solution. First you must heat water and then add sugar to the saturation point. As the water cools the sugar loses solubility and precipitates out of the solution, forming sweet crystals.
Similar to solid solutes, gases have solubility that is dependent on temperature and pressure.
Unlike ionic salts, the solubility of generally gases decreases with temperature. The higher the temperature the faster the gas molecules move and thus have a greater chance of escaping the liquid and evaporating.
High pressure can force a gas to dissolve into a liquid. Carbonated drinks like sodas are bottled at pressures greater than 1 atm. When the bottle is opened the pressure is released and the gas can escape.