common-ion effect
Picture a quiet pond that already has a lot of ducks. Try to release a few more of the same ducks into it and they will not all want to go — the crowd pushes back. The common-ion effect is the chemical version: if a solution already contains one of the ions that a salt or weak acid would release, then that salt dissolves less, or that acid ionises less, than it would in plain water. The crowd of identical ions discourages more from forming.
More precisely, the common-ion effect is the shift in an equilibrium caused by adding an ion that already appears in that equilibrium. It is simply Le Chatelier's principle applied to ions: adding a product (the shared ion) pushes the dissolving or ionising equilibrium backward. So adding a soluble chloride salt reduces the solubility of another chloride; adding a salt of a weak acid's anion suppresses that acid's ionisation.
It matters a great deal in practice — it is the engine behind buffer solutions, which resist pH change precisely because a common ion holds a weak acid's ionisation in check, and it is used to make sparingly soluble salts precipitate more completely. The honest caveat is that at high salt concentrations the simple picture breaks down: ionic-strength effects can actually increase solubility (the 'salting-in' effect), so the common-ion rule is a first approximation, not the last word.
Silver chloride is only slightly soluble: AgCl(s) ⇌ Ag+ + Cl−. Add sodium chloride, which floods the solution with Cl−, and the equilibrium retreats to the left — far less silver chloride dissolves than in pure water. That is the common-ion effect at work.
A shared ion already present pushes the equilibrium back.
The common-ion effect lowers solubility and suppresses weak-acid ionisation, but at very high ionic strength the opposite 'salting-in' can occur. Treat the simple rule as accurate for dilute solutions only.