A saturated solution is no longer capable of dissolving added solute; this means that, from this point on, any added solute will become visible in the solvent as chunks of undissolved particles. A saturated solution has no undissolved particles, just like an unsaturated one, but no more solute can be dissolved from this point on.There is a dynamic equilibrium between the dissolving and the re-crystalization of the solute.
A supersaturated solution is made by adding more solute to a saturated solution. From this point on, undissolved solute particles wiil be visible in the solution. A solution becomes supersaturated if it contains more solute than it is capable of dissolving at a particular temperature and volume.
Here's an example of a supersaturated solution