Parallel resistor and capacitor in non-inverting voltage follower
The purpose of the resistor R2 is to eliminate the DC offset caused by the op-amp input bias currents. If the bias currents are exactly matched, then the voltage drop across each 1K resistor (R1 and R2) is the same and the output voltage is equal to the input voltage. 

Fine, but if the op-amp has significant input capacitance or there is a lot of stray capacitance on the traces then the feedback signal has a lag and the AC output may be higher than the input. In an extreme case (very high resistance and an op-amp with a lot of input capacitance), it could oscillate. Putting the capacitor across the resistor deals with that. 

1K is such a low value that this would typically not be a problem in practice.