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We start with the Pourbaix Diagram for Zinc.
There are two axes:
E / V(SHE)
pH
E / V(SHE) pH
For this diagram the concentration of ions is 10−6 mol dm−3
E / V(SHE)
pH
If the concentration of ions is changed to 10−4 mol dm−3 the region of stability of a particular ion changes.

Hence, the lines representing equilibrium between two species also change.

Here the lines of equilibrium at two different concentrations are shown:

— 10−6 mol dm−3
— 10−4 mol dm−3
E / V(SHE)
pH
We can add lines for another concentration...

— 10−6 mol dm−3
— 10−4 mol dm−3
— 10−2 mol dm−3
E / V(SHE)
pH
And another...

— 10−6 mol dm−3
— 10−4 mol dm−3
— 10−2 mol dm−3
— 1 mol dm−3
E / V(SHE)
pH
Now imagine drawing the lines for each concentration on a separate sheet and stacking them one infront of the other.

This is equivalent to adding a third axis to the diagram:
E / V(SHE) pH log(concentration)
E / V(SHE)
pH
The four colours represent slices through a 3D space, at different concentrations.
E / V(SHE) pH log(concentration)
E / V(SHE)
pH
The variations seen as concentration changes are continuous, so they can be represented by planes.
E / V(SHE)
pH
The variations seen as concentration changes are continuous, so they can be represented by planes.
E / V(SHE)
pH
Now, a volume represents the conditions under which a particular species is thermodynamically stable.

The volume highlighted in blue indicates the conditions under which Zn(OH)2 is thermodynamically stable.
E / V(SHE)
pH
A plane now indicates the conditions at which an equilibrium between two species exists.

The plane highlighted in orange indicates the equilibrium between HZnO2− and ZnO2− ions.

This equilibrium is independent of concentration, therefore the plane is parallel to the concentration axis.