To put it more concretely:
Let's say Ksp of AgCl was 12 (I know, it's far from that; just for argument's sake). I dissolve 6 mols of AgNO3 in 1 L of water, then I add NaCl. AgCl will start precipitating once I add more than 2 mols of NaCl. Ksp=[Ag][Cl]=12=6*2. If instead of having dissolved 6 mols of AgNO3 I only dissolved 4, then I may add 3 mols of NaCl without seeing any precipitate. Ksp is the solubility product.
The "molar solubility" is just the maximum number of mols of AgCl that I can put into water without seeing precipitate. In this case, we have equal numbers of mols of Ag and Cl. Since Ksp of AgCl is 12, then [Ag]=[Cl]=(12)^.5 This is your molar solubility.