How does this capacitor discharge?
It will discharge when the +Vcc is switched off. The left plate is then connected to the ground via the power supply. The RST input then becomes -Vcc with respect to the ground and discharges via the resistor. 
+Vcc present:



+Vcc not present:



When the capacitor is charged the left plate is +5V with respect to the right plate. Since the +5Vcc power supply is connected to the left plate of the capacitor with the opposite polarity, the RST pin is +5v-(+5V) = 0V. However when you cut the power supply the left plate is connected to the GND (0V). RST then becomes 0V - (+5V) = -5V.