The specific heat of a substance is the amount of energy required to raise one gram of the material by one degree centigrade. But what happens if you get an ice cube too hot?  It is no longer an ice cube.  Changing the energy within a substance changes the temperature which can lead to a change in state of the substance.  A gas cools to become a liquid, and then cools further to become solid.

During a phase change the energy of the substance will change.  In changing from a liquid to a gas the heat that must be absorbed is the heat of vaporization. 

The reverse is also true.  The heat of vaporization is the amount of heat released when a substance changes from a gas to a liquid.

The quantity of heat needed to turn solid to liquid is called the heat of fusion. Again, the reverse is true.  The heat added to turn solid into liquid is the heat which needs to be removed to turn liquid into solid.

Since the amount of heat needed to vaporize a certain amount of liquid depends on how much liquid you have, heats of vaporization and fusion are written in J/g.  The total quantity of heat is written as