Charge Pump Circuit explaination
Similar circuits are used to make a charge pumps (switching with capacitors) to give you more than what your voltage rail can provide. Some DC-DC converters use circuits similar to this to boost the voltage rail for driving N-ch mosfets. With N-ch mosfets the gate voltage needs to be more than the source voltage (Vgs) for the mosfet to be able to turn on. The cool thing about mosfets is the gate needs a voltage (it's a capacitor) so the current is mimimal to get the mosfet to turn on. 

In this circuit the switches are driven external to the circuit, so you would need additional circuitry to drive the switches. The switches all switch at the same time. 


  How did the mosfet turn on to let that through?


The switches turn off and then the capacitor starts to charge the gate (remember the gate voltage would start to charge at Vs and V source of the mosfet would be 0V, so Vgs would still be enough to turn the mosfet on).

As the mosfet turns on, the capacitors negative terminal is always higher than the source of the mosfet, so the mosfet will always be on.