Whatever state the circuit is in is maintained by the 4k7 resistor's feedback, that much you understood, Silverwolf.
1) With the switch open the only input to the first inverter is the 4k7 resistor, whose feedback maintains the current state of the flip flop.
2) While the switch is open, the 220k resistor charges the capacitor (slowly) to the level of the first inverter's output (the inverse of the current circuit output).
3) When the switch is closed, the capacitor voltage (which by now is the same as inverter 1's output) is applied to inverter 1's input, thus flipping the circuit state.
4) While the switch is closed, the 4k7 resistor, being small compared to the 220k, charges (quickly) the capacitor to the level of the second inverter's output, which makes the circuit stable again. Goto 1.
Any clearer now?