Consider a capacitor consisting of two parallel conducting plates with an insulator in between.
Its capictance is C = ε0εr A/d
where εo is the dielectric constant of the vacuum, εr is the dielectric constant of the insulator, A is the area of the plates, and d is the distance between them.
Any one of these three variables can be changed by the displacement. However only variations of εr and the area overlap will produce a linear response.