What do the two series-connected, forward biased diodes do?
At a 'moderate' current (set by R1) a single Si diode drops ~ 0.6V, two in series drop  1.2V. Hence the voltage at the top of the potentiometer is ~ 1.2V, more or less independent of the battery voltage.

The rest of the circuit serves to get a constant current through the laser diode: the OpAmp will vary its output to get the same voltage on its two inputs, hence the voltage across the resistor R4 will equal the voltage set by the potentiometer. If the voltage across R4 is fixed so is the current, which is the same as the current through the laser (minus the much smaller base current for Q1).