Initially, both sides of the capacitor are high.
Switching the bottom side (blue) to low results in a momentary drop to 0 at the top side (green); the capacitor then starts charging and green eventually returns to 9.
Switching the bottom side (blue) back to high results in a momentary jump to 18 at the top (green), the capacitor starts discharging and green eventually returns to 9.
The brief pulse to 0 (when switching off) is sufficient to trigger a 555. This can be exploited to create a daisy-chain of monostable 555s.
I saw this configuration in the TI NE555 datasheet and Platt's MAKE: Electronics, where a few 555s are changed like this, but I simply couldn't figure out what was going on until I saw simulation.
