So the potential difference, or the voltage, is simply a measure of how much work has to be done, to get from one point to the other, or how much of this work is stored in the separate electrons, which want to go back to the positive side. Think of it as the free electrons really want to go to the positive side, but can't, as in the case of a battery, but as soon as there is a closed circuit the electrons will move to the positive terminal.
This is also the case for a battery, there is a potential difference across the two terminals, because near the negative terminal there is a lower electric potential than at the positive terminal. The potential difference is simply the work that has to be done to bring a unit charge from one terminal to the other.
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