Latent Heat of Vaporization:
The quantity of heat energy required to turn unit mass of a liquid into its saturated vapor at the same temperature. (Because the heat is given back if the vapor returns to the liquid state, and because it does not contribute to the temperature of the vapor, it is said to be "latent," - "Concealed: not visible or apparent: dormant, underdeveloped"Chambers Dictionary - hidden in the vapor.)
Latent Heat of Fusion:
The quantity of heat absorbed when bodies pass from the solid into the liquid state.
The concept might be generalized to any change of state, for example from gas to plasma.
Internal and External Latent Heat:
(The following is a little Bowdlerized, Sporus believes a more correct understanding is given by: Evaporation and Cooling, which see.) Imagine a lump of liquid evaporating into a gas. The particles - atoms or molecules - must attract each other, at close range, otherwise they could not hold together as a liquid. When a mass point evaporates away from the lump its potential energy rises therefore: like a ball thrown upwards into the air. Part of the latent heat - the internal latent heat - provides this potential energy. The remainder of the latent heat is the external fraction: In changing into a gas the liquid has undergone a large increase in its volume. The atmosphere must have been pushed back to make room for this new volume. Pushing something which resists through a distance requires work energy - the external fraction provides this.
(The latent heat in the vapor is all in the form of potential energy. This is the reason it makes no contribution to the temperature of the vapor.)