Here's why:
* Joule (J) is the unit of energy.
* Coulomb (C) is the unit of electric charge.
Therefore, joule per coulomb represents the energy per unit charge, which is precisely the definition of electric potential.
Think of it this way: if you move a charge of 1 Coulomb through an electric potential difference of 1 Volt (which is 1 Joule/Coulomb), you have done 1 Joule of work.