What is meant by the solubility of a substance?

and

What conditions must be specified when expressing the solubility of a substance

Solubility is the property of a substance (any state of matter) to whether it can be dissolved. So if a substance is soluble (i. e. salt - in water) it dissolves easily. If it is insoluble, then it does not dissolve.

Conditions that must be specified include the solute (the substance that is dissolved, such as the salt) and the solvent (the liquid in which the solute is dissolved).