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You actually already saw it in Newtonian mechanics via gravity. Observe:
In planetary motion, we say that the larger mass exerts a gravitational potential of the form
where this potential is what a massive object continuously "falls" toward. Seeing the similarities to electricity yet?
Now we define an electric potential of the form
This has a similar function as the gravitational potential, however now the charge can either "fall" toward the larger charge, or be repelled. Unlike gravity, charges usually don't have an initial angular momentum locking them into orbit. Nonetheless the equations are similar.
This electric potential serves as the voltage in electric circuits. You'll often hear the language "voltage drop" used, because a voltage (energy) differential is applied across two terminals, causing a high-energy region (+) to deliver its energy (via electrons) to the low-energy region (-). Voltage is just a more convenient way to handle energy.
