Essentially, K_"sp"Ksp is another equilibrium constant, which measures the solubility of insoluble and sparingly soluble salts.
For an insoluble salt, we may represent its dissolution reaction in this fashion:
MX_2(s) rightleftharpoonsM^+ + 2X^-MX2(s)⇌M++2X−
And its equilibrium reaction may be quantified:
([M^+][X^-]^2)/([MX_2(s)])[M+][X−]2[MX2(s)] == K_"sp"Ksp
But you can't have the concentration of a solid, i.e. [MX_2(s)][MX2(s)] is removed from the equilibrium expression, to give finally:
[M^+][X^-]^2[M+][X−]2 == K_"sp"Ksp
K_"sp"Ksp values have been measured for a host of sparingly soluble and insoluble salts under standard conditions. If M^+M+ in the above expression were a precious metal, addition of excess X^-X− to solution could salt the metal out for recovery.