It measures the highest amount of substance mixed into a liquid solvent while they are both at equal amounts. When the two mix together it is called a saturated solution. Certain substances can mix into any amount of a liquid solvent. An example of this is ethanol in water. This process is better described as "miscible" (the ability to mix with one another). Solubility does not depend on the size, in fact even the large particles will eventually all dissolve.
A solute is a substance that is dissolving in a solvent and is the smaller part of the solution. A solvent is the bigger part of a solution and is the substance that the solute dissolves in.
Solubility Facts for Kids. Kiddle Encyclopedia.