PWM circuit explanation
This circuit acts as a self powered AC switch. The circuit must have the lamp attached to function.

The IRF830 is acting as the switch here and is either on or off. As you can see, although a MOSFET if not designed for AC, since it is connected through that diamond shaped bridge rectifier, the load current always flows one way through the MOSFET. The MOSFET will normally be turned off by the pull down resistor R2.

D6, and R5 tap off some DC current to create a high voltage raw power supply. This high voltage level is then reduced through R4, R2 and D1 to produce a 10V supply that is maintained on C1.

When the Arduino lights the LED the phototransistor uses that 10V to charge the gate of the MOSFET turning it on.

NOTE: When the MOSFET is on, there will no longer be any voltage available to keep C2 and C1 charged. As such I suspect this circuit is controlled by some form of PWM, hopefully with the aid of some form of zero crossing detector, so that the MOSFET is turned off long enough to maintain the 10V on capacitor C1. If not, the lamp will turn out when C1 discharges or worse (See warning 2).

Also note that the return current for all this is the lamp. When off the current will be small, not enough to heat the lamp filament, but the lamp socket is still very much live.

As for the values, the 10V zener maintains sufficient voltage to ensure the MOSFET turns on adequately, R3 and R4 limit how much current is fed to that zener so it does not burn out. The values for the caps R2 will be what the designer deemed adequate for whatever AC frequency this was designed for. C2 is actually undersized in that schematic. If should be at least a 350V part.

WARNING 1: First and foremost, the circuit is lethal to work on. If you plan on building this use extreme caution. 

WARNING 2: Second, as I mentioned the thing loses power if you keep the LED lit too long. As such the gate voltage will fall and the MOSFET will enter the linear region till enough voltage is across it to keep the gate alive. It will then get VERY hot and may destroy itself or even catch fire. This is a design flaw with this circuit.