Solubility
Definition
How much of a substance can dissolve in a given amount of solvent: the limit that defines saturation.
Technical definition
Solubility is the maximum amount of solute that dissolves in a given quantity of solvent at a specified temperature (and pressure for gases), usually expressed in g/100 mL or mol/L. It reflects the balance of solute-solvent versus solute-solute and solvent-solvent interactions.
Example
Table salt's solubility is about 36 g per 100 mL of water at 20 C. Sugar's is about 200 g per 100 mL, which is why sugary drinks can be so sweet.
Common confusion
Solubility is temperature-dependent and solute-specific. Insoluble in textbooks usually means very slightly soluble, which is where Ksp applies, not literally zero.