Let's take a sparingly soluble salt, PbCl_2, for which K_(sp)=5.89xx10^(−5) at 25 ""^@C.
We can write the solubility expression as follows:
PbCl_2(s) rightleftharpoons Pb^(2+) + 2Cl^-
K_(sp)=5.89xx10^(−5)=[Pb^(2+)][Cl^-]^2, and if we represent the "solubility of lead chloride" under these conditions as S, then K_(sp)=5.89xx10^(−5)=Sxx2S^2=4S^3. We could usually solve this for S fairly easily.
Now that's the solubility product. However, there are scenarios when the ion product is greater than K_(sp), i.e. if we did the reaction in a salt solution, where [Cl^-] was artificially high. Because this ion product > K_"sp", "lead chloride" would precipitate from solution until the ion product -=K_"sp". Such a process is normally called "salting out", and if the metal were precious, say a salt of gold, or rhodium, or iridium, we would want to "salt out" the metal species so as maximize recovery of the metal.
See https://socratic.org/questions/what-is-ksp-in-chemistry for another treatment of the problem.
