Heat is a form of energy - just like light, sound or energy of movement.
The SI (International System of Units) standard energy unit is Joules, but people frequently use calories (for example, for foods - the 'caloric' amount is the amount of energy it provides).
Heat should not be confused to temperature. Temperature is a state of matter - it is actually resulted from vibration of the molecules of some object. When changing temperature, bodies exchange heat - they give or take energy to/from other bodies.