Many materials, like water, can exist in different "phases" - solid, liquid and gas.
Within any one phase we expect the temperature to increase if we add thermal energy ( e.g. by heating it with a Bunsen burner or putting it in a microwave.
The Specific Heat Capacity (or just "Specific Heat") is a measure of how much thermal energy [ in Joules ( J ) ] is required to raise the temperature of a unit mass ( 1kg ) by a temperature of 1 Kelvin ( 1 K ). It is measured in Joule per kilogram Kelvin ( J / kg.K )
However, it is found that while a substance is changing phase (provided the pressure is maintained constant) the temperature will remain constant (at the melting point or boiling point) despite the fact that thermal energy has to be increased in order to change the phase from solid to liquid, or from liquid to gas.
The Latent Heat of Fusion is the amount of thermal energy in Joules that is required to change a unit mass ( 1 kg ) of the solid into the same unit mass of the liquid without any increase of temperature (e.g. so change 1kg of solid ice at 273 K to 1kg of water at 273 K )
Similarly: The Latent Heat of Vaporization is the amount of thermal energy in Joules that is required to change a unit mass ( 1 kg ) of the liquid into the same unit mass of the gas without any increase of temperature (e.g. to change 1kg of water at 373 K to 1kg of steam at 373 K )
The Latent Heat Capacity (or just "Latent Heat") is measured in Joule per kilogram ( J / kg ).
-- Best wishes - Majikthise.
SPECIFIC HEAT CAPACITY is the quantity of heat required to raise the temperature of a unit of mass of a substance by a unit change in temperature. But, SPECIFIC LATENT HEAT CAPACITY (equation Q=mL) is the amount of energy needed to change to the state of a substance either from solid to liquid, liquid to gas without changing it's temperature