How can a saturated solution become supersaturated?
Let's imagine we're talking about a solid dissolved in a liquid. A saturated solution can become supersaturated when it is cooled.
Let's think about why this is true...
The solubility of solid solutes in liquid solvents increases as the solvent is warmed up. For example, you can dissolve more sugar in warm water as opposed to cold water.
Imagine a saturated solution of sugar water at 50 Celcius. Let's say it has "x" grams of sugar dissolved in it. The solubility of sugar will be lower at a lower temp. Let's say it is "y" grams at 25 Celcius. The value of x > y. When the water is cooled to a lower temp, it still has "x" grams dissolved, so it is now supersaturated.
Eventually the sugar will crystallize and form rock candy. For crystal formation to occur, rough or uneven surfaces are the best location. So if you want to make a supersaturated solution, a new glass container with no scratching or etching will be the best choice to slow the process of crystallization.