My teacher keeps talking about solubility. What does that mean, anyway?

Although some solutions, like one consisting of water and ethyl alcohol, can have any intermediate composition between the pure components, most solutions have an upper limit to the concentration of the solute. That limit is called the solubility of the substance.  For example, in a liter of water the maximum amount of calcium sulfate that can dissolve is 0.667 grams, which is 0.0049 moles of that solute. Therefore, the solubility of calcium sulfate may be reported either as 0.667 grams per liter or as 0.0049 M.