Solubility is the ability of a substance (the solute), to mix into a liquid (the solvent).
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.