In a capacitive position sensor, the electrified plate is the sensor surface and the second plate is the target. The electronics continuously change the voltage on the sensor surface.
This is the excitation voltage. The amount of current required to change the voltage is detected by the electronics and indicates the amount of capacitance between sensor and target.
An AC bridge circuit or other active electronic circuit is typically used to convert the capacity change into a current or voltage signal and output.

In ordinary capacitance-based position measurement, the size of the sensor and the target, and the dielectric medium (usually air) remain constant. The only variable is the gap.
All changes in capacitance are therefore the result of a change in the position of the target relative to the sensor. The driver is calibrated and the output scaled to provide a specific voltage for a corresponding change in capacitance (i.e., gap or displacement).