The amount of heat required to melt (or vapourize) 1 kilogram of a substance. The same amount of heat is released when 1 kilogram of the same substance freezes (or condenses). The heat is absorbed at constant temperature, the melting temperature.
Amorphous solids, including many polymers, do not have a sharp melting point. When these pass from a solid state to one which is fluid they do so over a wide temperature range, centred roughly about the glass temperature. It is then not appropriate to define a latent heat of melting.