It's a lamp dimmer...
Let's start with X2 - it is being used as a comparator to detect zero crossing. You can see where the + input is SLIGHTLY higher than ground. When the waveform slightly crosses 0V, the comparator switches. When it does, it triggers the transistor to short out the timing capacitor.
X1 is an integrator or ramp generator. It charges up on C2 and creates a ramp that is reset by X2 (above).
X3 is another comparator and triggers when the ramp voltage gets to the voltage set on the + input. Thus there is a delay caused by the ramp voltage and this turns the lamp on at some time after zero crossing. The delay is adjustable with VR1.
The lamp turns on at some point after zero crossing and turns off at the next zero crossing. Maybe it's easier to think about as: the lamp turns off at every zero crossing and turns back on after some delay. Given the full wave rectifier, this happens on every half cycle or twice the nominal line frequency.
Something like that...
Just take apart each of the 3 op amp blocks and analyze them separately. Zero crossing detector, ramp generator, delay/switching.