How it works - electric part

Math 

How Capacitance Relates to Distance

1. Size of the plates: As the plate size increases so does the capacitance.
2. Gap Size: capacitance decreases as the gap increases
3. Material between the plates (the dielectric): Dielectric material will cause the capacitance to increase or decrease depending on the material.

C=\dfrac{Area \cdot Dielectric}{Gap}

Capacitance is determined by Dielectric (the material in the gap) Area, and Gap. Capacitance increases when Dielectric or Area increase. Capacitance decreases when the Gap increases.

Calculate total sensor capacitance (CX)

When finger is present the total sensor capacitance (CX) is defined by equation 

 CX = CP + CF 

 where CF is finger's capacitance and CP is the sum of the distributed capacitance on the sensor. This is how sensor can calculate if the finger is on the sensor as seen in figure 1. This capacitive is then converted into digital values called Raw Counts which was explained on Position sensor page. 

Figure 1

Sources

1. http://www.analog.com/library/analogdialogue/archives/40-10/cap_sensors.html
2. http://www.capacitive-sensing.com/capacitive-sensor-theory.html