The joule per mole (symbol: J·mol-1 or J/mol) is an SI derived unit of energy per amount of material. Energy is measured in joules, and the amount of material is measured in moles. For example, Gibbs free energy is quantified as joules per mole. It is also a SI derived unit of molar thermodynamic energy defined as the energy equal to one joule in one mole of substance. 
Since 1 mole = 6.02214076×1023 particles (atoms, molecules, ions etc.), 1 joule per mole is equal to 1 joule divided by 6.02214179×1023 particles, or (6.022×10^23 particles/mole), 1.66054×10-24 joule per particle. This very small amount of energy is often expressed in terms of a smaller unit such as the electronvolt (eV, see below).
Physical quantities measured in J·mol-1 usually describe quantities of energy transferred during phase transformations or chemical reactions. Division by the number of moles facilitates comparison between processes involving different quantities of material and between similar processes involving different types of materials. The precise meaning of such a quantity is dependent on the context (what substances are involved, circumstances, etc.), but the unit of measurement is used specifically to describe certain existing phenomena, such as in thermodynamics it is the unit of measurement that describes molar energy.
For convenience and due to the range of magnitudes involved these quantities are almost always reported in kJ·mol-1 rather than in J·mol-1. For example, heats of fusion and vaporization are usually of the order of 10 kJ·mol-1, bond energies are of the order of 100 kJ·mol-1, and ionization energies of the order of 1000 kJ·mol-1.