The circled diode provides a -0.7Vdc negative rail or reference. Note that the anode of the diode is connected to circuit ground (mostly hidden by your red circle - but visible at high magnification).
This negative rail allows the (+) input of the 2nd op-amp to operate near or below ground.
Note that I would connect pin 4 of the op-amp to the cathode of the circled diode - this will improve operation when the (+) input of the 2nd op-amp is near zero Vdc.
I'm not certain what your circuit is attempting to do, but when you see a diode in parallel with a base-emitter of a transistor (Q1), then this is usually to add a small voltage drop. The base-emitter is a similar diode junction, so the circuit is usually matching voltage drops.
This technique can reduce effects such as crossover distortion in some types of opamp-driven circuits that require a transistor, making the circuit overall more 'ideal' in behavior.