The enthalpy of fusion of a substance, also known as (latent) heat of fusion, is the change in its enthalpy resulting from providing energy, typically heat, to a specific quantity of the substance to change its state from a solid to a liquid, at constant pressure. For example, when melting 1 kg of ice (at 0°C under a wide range of pressures), 333.55 kJ of energy is absorbed with no temperature change.
If ice did not have high latent heat of fusion,then ice would melt fastly at even room temperature.
i.e we require only less amount of energy to convert it from ice to liquid.
For example,normally when you take ice cubes from refrigerator,it would stay for some time before melting.
If it did not have high latent heat of fusion,then ice would melt immediately after taking the ice cubes from refrigerator.