Can someone explain how this circuit works? I have an idea but I dont know if its correct
How does the cap empty to 0V fast?


The diode across the 4k7 resistor fast discharges the capacitor that was previously slowly charged via the 4k7 resistor during the period when the 555 outputted a high pulse. The 555 output goes low after some time and rapidly discharges the capacitor via the diode.

In all other respects your simple analysis appears correct.