Optoisolated Feedback Pin Operation
The feedback is usually analog.  The opto-coupler is normally a package containing a LED driving a photo-transistor.  The amount of electrical coupling between the input LED and output photo-transistor is expressed in a term called "Current Transfer Ratio" or "CTR" for short.

What this means is that the current being passed through the photo-transistor is proportional to the amount of current passing through the LED that is driving the photo-transistor.  A CTR of 100% means that if 1 mA is passing through the LED, the photo-transistor is also passing 1 mA.  Because the current can vary smoothly between two extremes (full-off to full-on), this is considered to be analog.

The exact value of CTR isn't critical.  What is important to understand that the amount of current passing through the LED affects the amount of current being passed by the photo-transistor.

The opto-coupler is used as the isolation barrier in a power supply feedback circuit.  The power-supply is normally configured to raise the output voltage higher when the current from the photo-transistor in the opto-coupler is lower.  The power supply will run wide open if the photo-transistor is full OFF and will shut down when the photo-transistor is conducting as much current at it can (fully saturated).

The LED in the opto-coupler is driven by a circuit on the output side of the power supply such that the LED turns OFF when the output voltage is way too low and turns on hard when the output voltage is way too high.  The feedback is arranged such that the current through the LED is at some nominal value when the power supply is in regulation.

The circuit that drives the LED generally has a fair amount of gain.  What I mean by that is that a small change in output voltage results in a large change in LED current.  You don't want infinite gain - this would lead to instability.  But in general, you need enough gain so that the output stays at the desired value "close enough".

This circuit can be as simple as a zener diode in series with the opto-coupler and a current-limit resistor.  The current-limit resistor simply protects the LED if the output voltage should go too high for whatever reason (transient, etc).  However, this simple scheme suffers from initial accuracy problems as well as temperature-related changes.

The more common feedback controller is a TL-431 shunt regulator with the opto-coupler LED in the anode circuit (also with series current-limit resistor).  The TL-431 is a programmable shunt regulator with a feedback pin that is maintained at a constant voltage of 2.5 Volts.  This feedback pin has a voltage divider that monitors the output voltage.  When the output go too high, the TL-431 turns on harder, driving more current through the opto-coupler LED, and thus back to the power supply controller on the high-side of the power supply.

Sound complicated but it's actually simple in concept.