What does it mean that each conductor is characterized by a constant value of potential? My book mentions this:

In a system of conductors of arbitrary size, shape and
  charge configuration, each conductor is characterised by a constant
  value of potential, but this constant may differ from one conductor to
  the other.

Here is a screenshot to give better context to the above lines:

 A: In an electrostatic field the surface of an ideal conductor has constant potential $\phi$ means  that the electric field intensity vector $\mathbf{E} = -\mathbf{grad}\phi$ is perpendicular to the surface at all points of the conductor.
A: The potential difference inside one conductor is zero. The potential is not. 
In particular, two conductors can have a potential difference between them, so the two conductors have different potentials. 
A: This is easy to understand. Inside and on the surface of any conductor, there has to be a constant electrostatic potential because any gradient in this potential is an electric field that would lead to currents which cannot be sustained in an electrostatic situation. Thus in any conductor charges redistribute in such a way that there is always a zero electric field inside the conductor. In typical conductors like metals, with high concentration of charge carriers surface charges build up to produce the constant potential, and thus zero electric field, inside and along the surface. 
