My understanding of electrostatics is based on the concept of charge and electric field. If each point in a region of space has a certain charge density associated to it, then by integrating Coulomb's law over space, we get a certain electric field vector at each point.
For example, I would describe a typical "two parallel plates" problem as two parallel plates, each of which has a charge density of 1 Coulomb per square inch.
However, a way of describing electrostatics problems that I see sometimes involves talking about voltages. Now, I understand voltage as the potential of an electric field, but I don't understand what it means to say that we have two parallel plates, and that one is "charged to 5V" and the other is "charged to 0V".
In terms of charge density functions and the electric fields that they generate, what does it mean to declare that a pair of plates is "charged to a potential difference of x volts"?