The amount of solute which can dissolve in a particular amount of solvent at a particular temperature to form a saturated solution is called the solubility of the solute.
Usually for solids Solubility is a function of temperature, so on decreasing the temperature solubility decreases and vise-versa. Therefore, if a hot saturated solution is cooled then more and more amount of solute will precipitate out and settle down at the bottom.