How much precipitation occurs for a given ionic product?
Solubility product is the product of concentration of ions that can be soluble / in aqueous ionic state under given set of conditions. When ionic product is more means, the remaining is not soluble. Only that amount precipitates out. Still there are ions in water, product concentration of which is exactly equal to solubility product.

For basic understanding of equilibrium constant, you can refer: http://www.adichemistry.com/physical/equilibrium/introduction/chemical-equilibrium.html