solubility product
Keep stirring chalk into water and at some point no more will dissolve — extra powder just sits at the bottom. At that crowded limit, ions are leaving the solid and rejoining it at the same rate, a standoff between dissolving and crystallizing. The solubility product tells you exactly how crowded the solution can get before that standoff sets in.
For a sparingly soluble ionic solid, the solubility product Ksp is the equilibrium constant for the solid dissolving into its ions. For a salt like AgCl it is simply Ksp = [Ag+][Cl-]: multiply the ion concentrations at saturation. A small Ksp means the solid barely dissolves; a larger one means it dissolves more. The pure solid itself does not appear in the expression, because its amount does not change the balance.
Ksp matters because it predicts when a precipitate will form: mix two solutions and if the product of the relevant ion concentrations exceeds Ksp, solid crashes out. This governs scale in pipes, the formation of kidney stones, and how minerals deposit. The caveat is that Ksp truly applies only to slightly soluble salts and assumes ideal behaviour — in crowded real solutions, other ions can shift the real solubility.
Silver chloride is famously insoluble, with Ksp ≈ 1.8 × 10⁻¹⁰. Pour silver-nitrate solution into salt water and a white solid of AgCl instantly clouds the mixture, because the ion product blows past Ksp.
If the ion product exceeds Ksp, the salt can dissolve no more and precipitates.
Adding a salt that shares an ion with the solid lowers its solubility — the common-ion effect. Dissolving silver chloride in salt water, where chloride is already abundant, leaves even less silver dissolved than in pure water.