Start the simulation and throw the switch. The right op amp ramps up voltage linearly (integrator) while the left op amp compares the output of the first op amp to the voltage being measured. When the reference voltage crosses the measured voltage, the left op amp's output goes high.
Meanwhile, a simple binary counter counts up. When the left op amp goes high, the current count is loaded into the LCD. Simultaneously, the counter is reset and the capacitor used to generate the reference voltage is drained. Then the whole process repeats. This results in a single-slope sawtooth reference voltage.
The NOR gates are just a latch circuit used to switch the comparators output from the counter's load pin (to update the LCD) to ground (to drain the capacitor) with some delay; otherwise the potential from the capacitor would prevent the LCD from updating.
