#"Saturation"# defines an equilibrium property: that the concentration of the solute in solution is the same as the concentration there would be in the presence of UNDISSOLVED solute.
And thus for an ionic solute, #MX#, in water we could write:
#MX(s) rightleftharpoonsM^(+) +X^(-)#
As for any equilibrium we could quantify this by measuring an equilibrium constant, #K_"sp"# #=# #[M^+][X^-]#, which is quoted for a specific temperature. The #"sp"# stands for #"solubility product"#, and it is measured for a variety of sparingly soluble and insoluble salts. Why? Well, suppose you were isolating precious metal salts, such as those of gold or platinum or iridium; you don't want to throw these salts down the sink. Likewise, if you had salts of lead or mercury or cadmium, you don't want to throw these salts away, for the reason that you might poison the waterways.
So if more solute were added to a solution at equilibrium, likely more precipitate would collect at the bottom of the flask.