Why? Because there is usually a specific and measurable equilibrium between dissolved solute and undissolved solute at a given temperature.
Saturation defines an equilibrium condition: the rate of solute dissolution is equal to the rate of solute precipitation; alternatively, the rate of going up into solution is equal to the rate of coming out of solution.
This saturation depends on temperature, the properties of the solvent, and the nature (the solubility of) the solute. A hot solution can normally hold more solute than a cold one. If this equilibrium condition is not reached, in the case of unsaturation, the solvent can dissolve more solute, but in the case of supersaturation, the solvent holds MORE solute than would be in equilibrium with undissolved solute.