molar solubility
If you keep stirring a solid into water until no more will dissolve, you reach a ceiling — the water is full. Molar solubility is just how much of the solid that ceiling represents, counted in moles: the number of moles of a substance that will dissolve in one litre of solution before it can hold no more.
It is the practical, hands-on answer to 'how soluble is this?', expressed in moles per litre. For a salt, molar solubility is closely tied to the solubility product: you can calculate one from the other through the equilibrium expression. A solid with a tiny Ksp has a correspondingly tiny molar solubility, since so few ions can coexist in solution before the solid stops dissolving.
In analysis, molar solubility is what actually decides how much of a precipitate slips away dissolved — the loss that can spoil a gravimetric result if it is large. The caveat is that molar solubility is not a fixed property of the salt the way Ksp is: it shrinks in the presence of a common ion, can grow with an inert background salt or a complexing agent, and shifts with pH and temperature. Always ask 'soluble under what conditions?'
From silver chloride's Ksp of 1.8 x 10^-10, its molar solubility in pure water is the square root of that, about 1.3 x 10^-5 mol per litre — but in 0.1 M chloride it falls roughly a thousandfold.
Molar solubility is computed from Ksp — and shifts with conditions.
Molar solubility (moles per litre) and solubility (often grams per litre) describe the same fact in different units. Multiply molar solubility by the molar mass to convert to grams per litre.