Ksp is a 'static' (not really) measure of the ratio of products to reactants at equilbrium (think Keq). The only difference is that since there are only solid reactants, and you don't look at immisceable solids in your equilibria ratios, the only components you care about are the products (numerator of Keq). So Ksp is what you're SUPPOSED to have at equilbrium in terms of ratio (think ratio of 1 man to 1 woman in a happy marriage).
That's where the name Ksp comes from. This differs from what you actually have going on. In any particular reaction mixture, you can have too many of the product ions. This means that your Ion Product (IP) are combined greater than what they should be (Ksp). Think of this as having the extra girlfriend on the side. you're only supposed to have 1 man and 1 woman, for a total product (Ksp) of 1x1=1. Instead you have 1 man and 2 women for a total Ion product (IP) of 2. In this case you've got too many females, and one will need to revert back to reactant (single) status.
As much as I'd hate to say this (kidding) EK is right.