What exactly is a solubility product, and what is its use?
If we take small particles of a sparingly soluble salt, say AgCl, then one or two particles may dissolve in water and a saturated solution is obtained pretty soon. Upon adding extra AgCl to the solution precipitation of AgCl starts. At this stage, you'll find an equilibrium is established between the dissolved and the undissolved AgCl.

$$\ce{AgCl(s) &lt;=&gt; Ag+ (aq.) + Cl- (aq.)}$$

And for this equilibrium if you're to find the equilibrium constant, let's call it  $K_{sp}$, you get:

$$ \ce{K_{sp} = [Ag+] \cdot [Cl-]} $$

(Both the concentrations are the ones taken at equilibrium.)

This $K_{sp}$ is called solubility product. It's useful to predict whether or not more solute can be dissolved in your solution or not. We do this by comparing it to something which is called the ionic product.