This circuit is very useful when you have a single action to toggle between 2 states. The main purpose is to alternate the output between HIGH and LOW.
In a nutshell, the way the system is designed, we will have the capacitor charged when the output is HIGH. Pressing the button, will increase the voltage in the voltage divider on pin 6-2 driving the flip flop of the 555 to change the output to LOW. That way, the capacitor will discharge.
Pressing the button again, you will drive the voltage divider to a voltage close to 0. Which will drive the flip flop in the 555 to change the output to HIGH. But that is not a volatile state. The state will remain latched and the button will only alternate between them
