The filter is a Sallen-key low pass filter. Since no current will flow into the opamp, the inverting terminal of the opamp will be at the output voltage, Vo.
If u label the node voltage between R1 and R2 as Vx, you can write
V0 = [1 /(R2C1s + 1)] * Vx
After that you should apply KCL at node Vx, and you can find Vo/Vi to find the transfer function, after which you put s = jω, and you will get the cutoff frequency and gain.
The gain is 1, and cutoff is ωo = 1/R√(C1C2)
The function of cap C2 is to provide feedback. This feedback must be effective only near the cutoff frequency. At low frequencies, the impedance is too large so there is little feedback. At the higher frequencies, there is feedback, but now C1 is effectively a short, so the output voltage is low (close to zero), and hence it doesn't affect the rest of the circuit.
[Discussions and dervations will be given in an filter book like Huelsman. I used Franco]