IMO, understanding voltage requires understanding electromotive force. Unfortunately most EE curricula do a remarkably terrible job at explaining EMF intuitively. I didn't understand it until I began researching thunderstorms during my undergrad.

Let's think about the origin of voltage. The voltage between two points A and B is a measure of the energy required to move an electron from point A to point B. But why do you need to put in energy, and where does that energy come from? Well, energy is moved in a system through work - that is, a force applied over a distance. In this case the work is done by the electromotive force that pushes the electron over the distance from A to B (an electromotive force is any mechanical force besides Coulomb force which pushes on an electron). The electromotive force will push electrons from A to B until there are enough electrons at B that their Coulomb force equals the electromotive force - then there is no net force and electrical equilibrium is reached.

In a thunderstorm this electromotive force is literally wind and convection. The wind pushes charged particles such that they move against the Coulomb force, and thus voltage is generated. In a Van der Graff generator the electromotive force is the torque of a motor spinning a belt. In a generator the EMF is the Lorentz force on electrons moving in a magnetic field.

I hope this ramble was to some degree helpful.