I have stumbled upon the below circuit. I can't understand why there is a capacitor in the positive and negative inputs. Can anyone please explain to me the purpose of the capacitor in this circuit and this circuit how work ?
In your circuit, that capacitor C2 does nothing.
Because it is in parallel with the voltage source V1.
So the voltage across the capacitor C2 will be the voltage set by V1.
All the current that flows into and out of the capacitor C2 will be supplied / absorbed by V1.
The other components in this circuit cannot "see" the influence of this capacitor as they are only connected to the capacitor through the net called "input" which has a voltage determined by... yes, V1.
The presence of C2 will only make sense if there is some resistance/impedance in series with V1. Then that series resistance and C2 form a simple low pass filter.
This isn't a very well designed circuit. For example there is a capacitance from the output of the opamp directly to ground (C1 in series with C3). Many opamps don't like this at all. Improve the design by adding a series resistor in series with C3 or C1 (or both).