Help understanding simple circuit - ADC0803LCN
The marked portion of the schematic is a voltage follower, a k a unity gain buffer. This presents a very high input impedance to the signal source, and a low output impedance towards its load i.e. any following stage. Output voltage of the op-amp precisely tracks input voltage.

In this particular case this voltage follower takes as input the voltage seen at the wiper of the potentiometer, and outputs the same voltage at the output, adding in a bit of low-pass filtering courtesy the 300 Ohm resistor and 0.1 uF capacitor. Thus the output is smoother and less prone to high frequency noise.

The reason it is needed here: If one were to directly connect a load of, say, 300 Ohms, between the wiper of the potentiometer and ground, this would act in parallel with the potentiometer, dragging its resultant voltage down below the desired SPAN/2. By loading the wiper with a very high impedance load, i.e. the op-amp, such change in the desired potentiometer output is avoided.