Original: Work and heat are processes which add or subtract energy, while the internal energy is a particular form of energy associated with the system. Thus the term "heat energy" for means "that amount of energy added as the result of heating" rather than referring to a particular form of energy.
Simplified: In short, the law of conservation of energy states that energy can not be created or destroyed, it can only be changed from one form to another, such as when electrical energy is changed into heat energy.