Purpose of this capacitor?
C2's purpose is providing negative feedback for higher-frequency signals, thereby attenuating them.

In other words, U1's configuration works as an active low-pass filter. Not by any means a steep one.

I have several problems with the shown schematic, though. They range from aesthetic (GND should always point downwards, full stop) to the functional (the input R1/C1 is a 15Hz wide Low-pass filter. What do the other stages do?) to the component choice (why use an offset-nullable, strobable high-bandwidth opamp, and then use none of the features nor more than 15 Hz of the bandwidth? The extreme input impedance means higher noise than necessary in this configuration; why a JFET as the second stage? Why are the used opamps more than 40 years old? Is this a 1970's design? Do the restrictions that led to that design still apply?). It's always good to evaluate the quality of your circuit sources.