The solubility product derives from the equilibrium expression for the solution process of a weak electrolyte in water. The equilibrium is heterogeneous. This means that the substances involved are not all of the same state of matter. The true equilibrium constant describing the saturated solution would contain the concentration of the solid undissolved salt in the saturated solution, in addition to the concentrations of the ions. Don't worry about that, though, because the concentration of the solid is a constant (it is literally the number of moles of in a liter of the solid salt) and it is bundled into Ksp.

Solubility product questions are one of the real sources of plug-and-chug type problems on the MCAT (questions where you may have a bit of arithmetic). Solution chemistry is one of the most important MCAT topics, and heterogeneous solution equlibrium is one of the most important subtopics of solution chemistry.

When you solve solubility product problems, beware of the most common pitfalls. Watch your coefficients and exponents! A weak electrolyte such as PbCl2 disassociates to form a single Pb++ for every two Cl- ions. This means, for example, that:

Ksp = [Pb++][Cl-]2

Furthermore, when you express the concentration of one of the ions in terms of the other:

2[Pb++] = [Cl-]