A saturated solution is when the maximum amount of solute that could be dissolved in that solvent volume at that temperature and pressure has been dissolved, adding more solute beyond this point would lead to the additional solute not dissolving in the solvent. When the maximum solute concentration in the solution that can be dissolved has been reached the solution is said to be saturated.
This would be the Melting point because it is showing that at a certain heat it melts so therefore it is the point it melts and therefore called the melting point