What is the purpose of this op amp?
Amplifier U1 helps to make the circuit as close to "ideal" as possible. In the pH cell the impedances involved re very high and any variations from ideality are reflected in the results. 

The "challenge" is given in the following section from the application note:


The output of amplifier U1, which
is set up in a unity-gain configuration, biases the reference
electrode of the pH electrode with the same voltage, 512 mV,
at low impedance. 

The pH-measuring electrode will produce
a voltage which rides on top of this 512 mV bias voltage. In
effect, the circuit shifts the bipolar pH-electrode signal to a
unipolar signal for use in a single-supply system.


ie any error in this voltage is directly reflected in the output voltage as an error in pH reading.

The source impedance of the 2 x 10 k resistors in series is 5 K ( Reffective = R1 x R2 / (R1+ R2)). If the cell were to load this with a 1 megohm impedance the change in actual voltage  would be 5k // 1 M = 0.005 = 0.5%. Loading with 10 Megohm would give 0.05% error etc. This does not sound much (&amp; isn't much) but the sensitivity of the cell is 1 mV per pH. So 5/1000 x 512 mV ~= 2.5 mV or 2.5 pH error. And 10 megohm loading = 0.25 pH error. Even 100 megohm loading = 0.025 pH error.  

If pH is read to even 0.1 pH units an error of 0.025 pH is 1/4 of a "bit". If pH was read to 0.01 units then 0.025 pH = 2.5 "bits " - and that's with 100 only megohm load!

Reducing R1 &amp; R2 to 1 k or 100 ohms would help, at the expense of increased current drain U1 provides a better solution at acceptable cost.